32nd International Symposium on Distributed Computing (DISC 2018), DISC 2018, October 15-19, 2018, New Orleans, USA
DISC 2018
October 15-19, 2018
New Orleans, USA
International Symposium on Distributed Computing
DISC
http://www.disc-conference.org/
https://dblp.org/db/conf/wdag
Leibniz International Proceedings in Informatics
LIPIcs
https://www.dagstuhl.de/dagpub/1868-8969
https://dblp.org/db/series/lipics
1868-8969
Ulrich
Schmid
Ulrich Schmid
Josef
Widder
Josef Widder
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
121
2018
978-3-95977-092-7
https://www.dagstuhl.de/dagpub/978-3-95977-092-7
Front Matter, Table of Contents, Preface, Conference Organization, Awards
Front Matter, Table of Contents, Preface, Conference Organization, Awards
Front Matter
Table of Contents
Preface
Conference Organization
Awards
0:i-0:xx
Front Matter
Ulrich
Schmid
Ulrich Schmid
Josef
Widder
Josef Widder
10.4230/LIPIcs.DISC.2018.0
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Autonomous Vehicles: From Individual Navigation to Challenges of Distributed Swarms (Invited Talk)
Recent years have seen impressive advancements in the development of robots on four wheels: autonomous cars. While much of this progress is owed to a combination of breakthroughs in artificial intelligence and improved sensors, dealing with complex, non-ideal scenarios, where errors or failures can turn out to be catastrophic is still largely unsolved; this will require combining "fast", heuristic approaches of machine learning with "slow", more deliberate methods of discrete algorithms and mathematical optimization. However, many of the real challenges go beyond performance guarantees for individual vehicles and aim at the behavior of swarms: How can we control the complex interaction of a distributed swarm of vehicles, such that the overall behavior can measure up to and go beyond the capabilities of humans? Even though many of our engineering colleagues do not fully realize this yet, there is no doubt that this will have to be based to no small part on expertise in distributed algorithms.
I will present a multi-level overview of results and challenges, ranging from information exchanges of small groups all the way to game-theoretic mechanisms for large-scale control. Application scenarios do not just arise from road traffic (where short response times, large numbers of vehicles and individual interests give rise to many difficulties), but also from swarms of autonomous space vehicles (where huge distances, times and energies make distributed methods indispensable).
Autonomous vehicles
interaction
robot swarms
game theory
Theory of computation~Distributed algorithms
Theory of computation~Algorithmic game theory and mechanism design
1:1-1:1
Invited Talk
Sándor P.
Fekete
Sándor P. Fekete
Department of Computer Science, TU Braunschweig, 38106 Braunschweig, Germany
https://orcid.org/0000-0002-9062-4241
10.4230/LIPIcs.DISC.2018.1
Sándor P. Fekete
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Challenges for Machine Learning on Distributed Platforms (Invited Talk)
Deep neural networks are trained by solving huge optimization problems with large datasets and millions of variables. On the surface, it seems that the size of these problems makes them a natural target for distributed computing. Despite this, most deep learning research still takes place on a single compute node with a small number of GPUs, and only recently have researchers succeeded in unlocking the power of HPC. In this talk, we'll give a brief overview of how deep networks are trained, and use HPC tools to explore and explain deep network behaviors. Then, we'll explain the problems and challenges that arise when scaling deep nets over large system, and highlight reasons why naive distributed training methods fail. Finally, we'll discuss recent algorithmic innovations that have overcome these limitations, including "big batch" training for tightly coupled clusters and supercomputers, and "variance reduction" strategies to reduce communication in high latency settings.
Machine learning
distributed optimization
Computing methodologies~Machine learning
2:1-2:3
Invited Talk
Tom
Goldstein
Tom Goldstein
University of Maryland, College Park, MD, USA
Support for this work was provided by DARPA Lifelong Learning Machines (FA8650-18-2-7833), the US Office of Naval Research (N00014-17-1-2078), the US National Science Foundation (CCF-1535902), and the Sloan Foundation.
10.4230/LIPIcs.DISC.2018.2
Soham De and Tom Goldstein. Efficient distributed SGD with variance reduction. In 2016 IEEE 16th International Conference on Data Mining (ICDM), pages 111-120. IEEE, 2016. URL: http://dx.doi.org/10.1109/ICDM.2016.0022.
http://dx.doi.org/10.1109/ICDM.2016.0022
Soham De, Abhay Yadav, David Jacobs, and Tom Goldstein. Automated inference with adaptive batches. In Aarti Singh and Jerry Zhu, editors, Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, volume 54 of Proceedings of Machine Learning Research, pages 1504-1513. PMLR, 2017. URL: http://proceedings.mlr.press/v54/de17a.html.
http://proceedings.mlr.press/v54/de17a.html
Hao Li, Zheng Xu, Gavin Taylor, and Tom Goldstein. Visualizing the loss landscape of neural nets, 2017. URL: http://arxiv.org/abs/1712.09913v1.
http://arxiv.org/abs/1712.09913v1
Tom Goldstein
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Logical Analysis of Distributed Systems: The Importance of Being Constructive (Invited Talk)
The design and analysis of complex distributed systems proceeds along numerous levels of abstractions. One key abstraction step for reducing complexity is the passage from analog transistor electronics to synchronously clocked digital circuits. This significantly simplifies the modelling from continuous differential equations over the real numbers to discrete Mealy automata over two-valued Boolean algebra. Although typically taken for granted, this step is magic. How do we obtain clock synchronization from asynchronous communication of continuous values? How do we decide on the discrete meaning of continuous signals without a synchronization clock? From a logical perspective, the possibility of synchronization is paradoxical and appears "out of thin air." The chicken-or-egg paradox persists at higher levels abstraction for distributed software. We cannot achieve globally consistent state from local communications without synchronization. At the same time we cannot synchronize without access to globally consistent state. From this perspective, distributed algorithms such as for leader election, consensus or mutual exclusion do not strictly solve their task but merely reduce one synchronization problem to another.
This talk revisits the logical justification of the synchronous abstraction claiming that correctness arguments, in so far as they are not merely reductions, must intrinsically depend on reasoning in classical logic. This is studied at the circuit level, where all software reductions must end. The well-known result that some synchronization elements cannot be implemented in delay-insensitive circuits is related to Berry's Thesis according to which digital circuits are delay-insensitive if and only if they are provably correct in constructive logic. More technically, the talk will show how non-inertial delays give rise to a constructive modal logic while inertial delays are inherently non-constructive. This gives a logical explanation for why inertial delays can be used to build arbiters, memory-cells and other synchronization elements, while non-inertial delays are not powerful enough. Though these results are tentative, they indicate the importance of logical constructiveness for metastable-free discrete abstractions of physical behavior. This also indicates that metastability is an unavoidable artifact of the digital abstraction in classical logic.
Hardware synchronisation
inertial delays
delay-insensitive circuits
constructive circuits
metastability
constructive modal logic
Theory of computation~Modal and temporal logics
Theory of computation~Constructive mathematics
Computing methodologies~Concurrent algorithms
Hardware~Hardware validation
3:1-3:1
Invited Talk
This work is partially supported by the German Research Council (DFG) under grant number ME-1427/6-2.
Michael
Mendler
Michael Mendler
The Otto-Friedrich University of Bamberg, Bamberg, Germany
10.4230/LIPIcs.DISC.2018.3
Michael Mendler
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Selecting a Leader in a Network of Finite State Machines
This paper studies a variant of the leader election problem under the stone age model (Emek and Wattenhofer, PODC 2013) that considers a network of n randomized finite automata with very weak communication capabilities (a multi-frequency asynchronous generalization of the beeping model's communication scheme). Since solving the classic leader election problem is impossible even in more powerful models, we consider a relaxed variant, referred to as k-leader selection, in which a leader should be selected out of at most k initial candidates. Our main contribution is an algorithm that solves k-leader selection for bounded k in the aforementioned stone age model. On (general topology) graphs of diameter D, this algorithm runs in O~(D) time and succeeds with high probability. The assumption that k is bounded turns out to be unavoidable: we prove that if k = omega (1), then no algorithm in this model can solve k-leader selection with a (positive) constant probability.
stone age model
beeping communication scheme
leader election
k-leader selection
randomized finite state machines
asynchronous scheduler
Theory of computation~Distributed computing models
4:1-4:17
Regular Paper
Yehuda
Afek
Yehuda Afek
Tel Aviv University, Tel Aviv, Israel
The work of Y. Afek was partially supported by a grant from the Blavatnik Cyber Security Council and the Blavatnik Computer Science Research Fund.
Yuval
Emek
Yuval Emek
Technion - Israel Institute of Technology, Haifa, Israel
The work of Y. Emek was supported in part by an Israeli Science Foundation grant number 1016/17.
Noa
Kolikant
Noa Kolikant
Tel Aviv University, Tel Aviv, Israel
10.4230/LIPIcs.DISC.2018.4
Karl R. Abrahamson, Andrew Adler, Lisa Higham, and David G. Kirkpatrick. Probabilistic solitude verification on a ring. In Proceedings of ACM Symposium on Principles of Distributed Computing (PODC), pages 161-173, 1986.
Yehuda Afek, Noga Alon, Ziv Bar-Joseph, Alejandro Cornejo, Bernhard Haeupler, and Fabian Kuhn. Beeping a maximal independent set. In Proceedings of International Symposium on Distributed Computing (DISC), pages 32-50, 2011.
Yehuda Afek and Yossi Matias. Elections in anonymous networks. Inf. Comput., 113(2):312-330, 1994.
Dana Angluin. Local and global properties in networks of processors (extended abstract). In Proceedings of ACM SIGACT Symposium on Theory of Computing (STOC), pages 82-93, 1980.
Dana Angluin, James Aspnes, Zoë Diamadi, Michael J. Fischer, and René Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Computing, 18(4):235-253, 2006.
James Aspnes and Eric Ruppert. An Introduction to Population Protocols, pages 97-120. Springer Berlin Heidelberg, 2009.
Hagit Attiya, Marc Snir, and Manfred K. Warmuth. Computing on an anonymous ring. J. ACM, 35(4):845-875, 1988.
Baruch Awerbuch. Complexity of network synchronization. J. ACM, 32(4):804-823, 1985.
Baruch Awerbuch. Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems. In Proceedings of ACM SIGACT Symposium on Theory of Computing (STOC), pages 230-240, 1987.
Sarah Cannon, Joshua J. Daymude, Dana Randall, and Andréa W. Richa. A Markov chain algorithm for compression in self-organizing particle systems. In Proceedings of ACM Symposium on Principles of Distributed Computing (PODC), pages 279-288, 2016.
Alejandro Cornejo and Fabian Kuhn. Deploying wireless networks with beeps. In Proceedings of International Symposium on Distributed Computing (DISC), pages 148-162, 2010.
Joshua J. Daymude, Zahra Derakhshandeh, Robert Gmyr, Alexandra Porter, Andréa W. Richa, Christian Scheideler, and Thim Strothmann. On the runtime of universal coating for programmable matter. Natural Computing, 17(1):81-96, 2018.
Zahra Derakhshandeh, Robert Gmyr, Andréa W. Richa, Christian Scheideler, and Thim Strothmann. An algorithmic framework for shape formation problems in self-organizing particle systems. In Proceedings of International Conference on Nanoscale Computing and Communication (NANOCOM), pages 21:1-21:2, 2015.
Zahra Derakhshandeh, Robert Gmyr, Andréa W. Richa, Christian Scheideler, and Thim Strothmann. Universal shape formation for programmable matter. In Proceedings of ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 289-299, 2016.
Zahra Derakhshandeh, Robert Gmyr, Andréa W. Richa, Christian Scheideler, Thim Strothmann, and Shimrit Tzur-David. Infinite object coating in the Amoebot model. CoRR, abs/1411.2356, 2014. URL: http://arxiv.org/abs/1411.2356.
http://arxiv.org/abs/1411.2356
Zahra Derakhshandeh, Robert Gmyr, Thim Strothmann, Rida Bazzi, Andréa W. Richa, and Christian Scheideler. Leader election and shape formation with self-organizing programmable matter. In Proceedings of International Conference on DNA Computing and Molecular Programming (DNA), pages 117-132, 2015.
Shlomi Dolev, Robert Gmyr, Andréa W. Richa, and Christian Scheideler. Ameba-inspired self-organizing particle systems. CoRR, abs/1307.4259, 2013. URL: http://arxiv.org/abs/1307.4259.
http://arxiv.org/abs/1307.4259
David Doty. Timing in chemical reaction networks. In Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 772-784, 2014.
Yuval Emek and Jara Uitto. Dynamic networks of finite state machines. In Proceedings of International Colloquium on Structural Information and Communication Complexity (SIROCCO), pages 19-34, 2016.
Yuval Emek and Roger Wattenhofer. Stone age distributed computing. In Proceedings of ACM Symposium on Principles of Distributed Computing (PODC), pages 137-146, 2013.
Michael J. Fischer, Nancy A. Lynch, and Michael S. Paterson. Impossibility of distributed consensus with one faulty process. J. ACM, 32(2):374-382, 1985.
Greg N. Frederickson and Nancy A. Lynch. Electing a leader in a synchronous ring. J. ACM, 34(1):98-115, 1987.
Robert G. Gallager, Pierre A. Humblet, and Philip M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst., 5(1):66-77, 1983.
M. Gardner. The fantastic combinations of John Conway’s new solitaire game `life'. Scientific American, 223(4):120-123, 1970.
Lauri Hella, Matti Järvisalo, Antti Kuusisto, Juhana Laurinharju, Tuomo Lempiäinen, Kerkko Luosto, Jukka Suomela, and Jonni Virtema. Weak models of distributed computing, with connections to modal logic. Distributed Computing, 28(1):31-53, 2015.
Alon Itai and Michael Rodeh. Symmetry breaking in distributed networks. Inf. Comput., 88(1):60-87, 1990.
Laurent Keller and Peter Nonacs. The role of queen pheromones in social insects: queen control or queen signal? Animal Behaviour, 45(4):787-794, 1993.
Jennie J. Kuzdzal-Fick, David C. Queller, and Joan E. Strassmann. An invitation to die: initiators of sociality in a social amoeba become selfish spores. Biology letters, 6(6):800-802, 2010.
Ivan Lavallée and Christian Lavault. Spanning tree construction for nameless networks. In Proceedings of International Workshop on Distributed Algorithms (WDAG), pages 41-56, 1990.
Othon Michail, Ioannis Chatzigiannakis, and Paul G. Spirakis. New Models for Population Protocols. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, 2011.
John Von Neumann. Theory of Self-Reproducing Automata. University of Illinois Press, Champaign, IL, USA, 1966.
David Peleg. Distributed Computing: A Locality-sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2000.
Baruch Schieber and Marc Snir. Calling names on nameless networks. Inf. Comput., 113(1):80-101, 1994.
Joanna M. Setchell, Marie Charpentier, and E. Jean Wickings. Mate guarding and paternity in mandrills: factors influencing alpha male monopoly. Animal Behaviour, 70(5):1105-1120, 2005.
Jonathan M.W. Slack. Essential developmental biology. John Wiley &Sons, 2009.
NSF workshop on self-organizing particle systems (SOPS). http://sops2014.cs.upb.de/, 2014.
http://sops2014.cs.upb.de/
Stephen Wolfram. A New Kind of Science. Wolfram Media Inc., Champaign, Ilinois, US, United States, 2002.
Yehuda Afek, Yuval Emek, and Noa Kolikant
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
The Role of A-priori Information in Networks of Rational Agents
Until now, distributed algorithms for rational agents have assumed a-priori knowledge of n, the size of the network. This assumption is challenged here by proving how much a-priori knowledge is necessary for equilibrium in different distributed computing problems. Duplication - pretending to be more than one agent - is the main tool used by agents to deviate and increase their utility when not enough knowledge about n is given.
We begin by proving that when no information on n is given, equilibrium is impossible for both Coloring and Knowledge Sharing. We then provide new algorithms for both problems when n is a-priori known to all agents. However, what if agents have partial knowledge about n? We provide tight upper and lower bounds that must be a-priori known on n for equilibrium to be possible in Leader Election, Knowledge Sharing, Coloring, Partition and Orientation.
rational agents
distributed game theory
coloring
knowledge sharing
Theory of computation~Distributed computing models
5:1-5:18
Regular Paper
This research was supported by the Israel Science Foundation (grant 1386/11).
https://arxiv.org/abs/1711.04728
Yehuda
Afek
Yehuda Afek
Tel-Aviv University, Tel-Aviv, Israel
Shaked
Rafaeli
Shaked Rafaeli
Tel-Aviv University, Tel-Aviv, Israel
Moshe
Sulamy
Moshe Sulamy
Tel-Aviv University, Tel-Aviv, Israel
10.4230/LIPIcs.DISC.2018.5
Ittai Abraham, Lorenzo Alvisi, and Joseph Y. Halpern. Distributed computing meets game theory: Combining insights from two fields. SIGACT News, 42(2):69-76, 2011. URL: http://dx.doi.org/10.1145/1998037.1998055.
http://dx.doi.org/10.1145/1998037.1998055
Ittai Abraham, Danny Dolev, Rica Gonen, and Joseph Y. Halpern. Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation. In PODC, pages 53-62, 2006. URL: http://dx.doi.org/10.1145/1146381.1146393.
http://dx.doi.org/10.1145/1146381.1146393
Ittai Abraham, Danny Dolev, and Joseph Y. Halpern. Lower bounds on implementing robust and resilient mediators. In TCC, pages 302-319, 2008. URL: http://dx.doi.org/10.1007/978-3-540-78524-8_17.
http://dx.doi.org/10.1007/978-3-540-78524-8_17
Ittai Abraham, Danny Dolev, and Joseph Y. Halpern. Distributed protocols for leader election: A game-theoretic perspective. In DISC, pages 61-75, 2013. URL: http://dx.doi.org/10.1007/978-3-642-41527-2_5.
http://dx.doi.org/10.1007/978-3-642-41527-2_5
Norman Abramson. The aloha system: Another alternative for computer communications. In Proceedings of the November 17-19, 1970, Fall Joint Computer Conference, AFIPS '70 (Fall), pages 281-285, New York, NY, USA, 1970. ACM.
Y. Afek, S. Rafaeli, and M. Sulamy. Cheating by Duplication: Equilibrium Requires Global Knowledge. ArXiv e-prints, 2017. URL: http://arxiv.org/abs/1711.04728.
http://arxiv.org/abs/1711.04728
Yehuda Afek, Yehonatan Ginzberg, Shir Landau Feibish, and Moshe Sulamy. Distributed computing building blocks for rational agents. In Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing, PODC '14, 2014.
Amitanand S. Aiyer, Lorenzo Alvisi, Allen Clement, Michael Dahlin, Jean-Philippe Martin, and Carl Porth. Bar fault tolerance for cooperative services. In SOSP, pages 45-58, 2005. URL: http://dx.doi.org/10.1145/1095810.1095816.
http://dx.doi.org/10.1145/1095810.1095816
Hagit Attiya and Jennifer Welch. Distributed Computing: Fundamentals, Simulations and Advanced Topics. John Wiley &Sons, 2004.
B. Awerbuch, M. Luby, A. V. Goldberg, and S. A. Plotkin. Network decomposition and locality in distributed computation. In Proceedings of the 30th Annual Symposium on Foundations of Computer Science, SFCS '89, pages 364-369, Washington, DC, USA, 1989. IEEE Computer Society. URL: http://dx.doi.org/10.1109/SFCS.1989.63504.
http://dx.doi.org/10.1109/SFCS.1989.63504
D. Bank, M. Sulamy, and E. Waserman. Reaching Distributed Equilibrium with Limited ID Space. ArXiv e-prints, 2018. URL: http://arxiv.org/abs/1804.06197.
http://arxiv.org/abs/1804.06197
Imre Bárány. Fair distribution protocols or how the players replace fortune. Math. Oper. Res., 17(2):327-340, 1992. URL: http://dx.doi.org/10.1287/moor.17.2.327.
http://dx.doi.org/10.1287/moor.17.2.327
Elchanan Ben-Porath. Cheap talk in games with incomplete information. J. Economic Theory, 108(1):45-71, 2003. URL: http://dx.doi.org/10.1016/S0022-0531(02)00011-X.
http://dx.doi.org/10.1016/S0022-0531(02)00011-X
Rajat Bhattacharjee and Ashish Goel. Avoiding ballot stuffing in ebay-like reputation systems. In Proceedings of the 2005 ACM SIGCOMM Workshop on Economics of Peer-to-peer Systems, P2PECON '05, pages 133-137, New York, NY, USA, 2005. ACM.
Monica Bianchini, Marco Gori, and Franco Scarselli. Inside pagerank. ACM Trans. Internet Technol., 5(1):92-128, 2005.
Alice Cheng and Eric Friedman. Sybilproof reputation mechanisms. In Proceedings of the 2005 ACM SIGCOMM Workshop on Economics of Peer-to-peer Systems, P2PECON '05, pages 128-132, New York, NY, USA, 2005. ACM.
Richard Cole and Uzi Vishkin. Deterministic coin tossing with applications to optimal parallel list ranking. Inf. Control, 70(1):32-53, 1986.
Varsha Dani, Mahnush Movahedi, Yamel Rodriguez, and Jared Saia. Scalable rational secret sharing. In PODC, pages 187-196, 2011. URL: http://dx.doi.org/10.1145/1993806.1993833.
http://dx.doi.org/10.1145/1993806.1993833
Yevgeniy Dodis, Shai Halevi, and Tal Rabin. A cryptographic solution to a game theoretic problem. In CRYPTO, pages 112-130, 2000. URL: http://dx.doi.org/10.1007/3-540-44598-6_7.
http://dx.doi.org/10.1007/3-540-44598-6_7
John R. Douceur. The sybil attack. In Revised Papers from the First International Workshop on Peer-to-Peer Systems, IPTPS '01, pages 251-260, London, UK, UK, 2002. Springer-Verlag.
Georg Fuchsbauer, Jonathan Katz, and David Naccache. Efficient rational secret sharing in standard communication networks. In TCC, pages 419-436, 2010. URL: http://dx.doi.org/10.1007/978-3-642-11799-2_25.
http://dx.doi.org/10.1007/978-3-642-11799-2_25
S. Dov Gordon and Jonathan Katz. Rational secret sharing, revisited. In SCN, pages 229-241, 2006. URL: http://dx.doi.org/10.1007/11832072_16.
http://dx.doi.org/10.1007/11832072_16
Adam Groce, Jonathan Katz, Aishwarya Thiruvengadam, and Vassilis Zikas. Byzantine agreement with a rational adversary. In ICALP (2), pages 561-572, 2012. URL: http://dx.doi.org/10.1007/978-3-642-31585-5_50.
http://dx.doi.org/10.1007/978-3-642-31585-5_50
Joseph Y. Halpern and Xavier Vilaça. Rational consensus: Extended abstract. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC '16, pages 137-146, New York, NY, USA, 2016. ACM.
L. Kleinrock and F. Tobagi. Packet switching in radio channels: Part i - carrier sense multiple-access modes and their throughput-delay characteristics. IEEE Transactions on Communications, 23(12):1400-1416, December 1975.
Fabian Kuhn and Rogert Wattenhofer. On the complexity of distributed graph coloring. In Proceedings of the Twenty-fifth Annual ACM Symposium on Principles of Distributed Computing, PODC '06, pages 7-15, New York, NY, USA, 2006. ACM. URL: http://dx.doi.org/10.1145/1146381.1146387.
http://dx.doi.org/10.1145/1146381.1146387
Matt Lepinski, Silvio Micali, Chris Peikert, and Abhi Shelat. Completely fair sfe and coalition-safe cheap talk. In PODC, pages 1-10, 2004. URL: http://dx.doi.org/10.1145/1011767.1011769.
http://dx.doi.org/10.1145/1011767.1011769
N. Linial. Legal coloring of graphs. Combinatorica, 6(1):49-54, 1986. URL: http://dx.doi.org/10.1007/BF02579408.
http://dx.doi.org/10.1007/BF02579408
Nathan Linial. Distributive graph algorithms global solutions from local data. In Proceedings of the 28th Annual Symposium on Foundations of Computer Science, SFCS '87, pages 331-335, Washington, DC, USA, 1987. IEEE Computer Society. URL: http://dx.doi.org/10.1109/SFCS.1987.20.
http://dx.doi.org/10.1109/SFCS.1987.20
Nathan Linial. Locality in distributed graph algorithms. SIAM Journal on Computing, 21(1):193-201, 1992. URL: http://dx.doi.org/10.1137/0221015.
http://dx.doi.org/10.1137/0221015
Anna Lysyanskaya and Nikos Triandopoulos. Rationality and adversarial behavior in multi-party computation. In CRYPTO, pages 180-197, 2006. URL: http://dx.doi.org/10.1007/11818175_11.
http://dx.doi.org/10.1007/11818175_11
Robert McGrew, Ryan Porter, and Yoav Shoham. Towards a general theory of non-cooperative computation. In TARK, pages 59-71, 2003. URL: http://dx.doi.org/10.1145/846241.846249.
http://dx.doi.org/10.1145/846241.846249
Thomas Moscibroda, Stefan Schmid, and Roger Wattenhofer. When selfish meets evil: byzantine players in a virus inoculation game. In PODC, pages 35-44, 2006. URL: http://dx.doi.org/10.1145/1146381.1146391.
http://dx.doi.org/10.1145/1146381.1146391
Rafael Pass and Elaine Shi. Hybrid Consensus: Efficient Consensus in the Permissionless Model. In 31st International Symposium on Distributed Computing (DISC 2017), 2017.
Rafael Pass and Elaine Shi. The sleepy model of consensus. In Tsuyoshi Takagi and Thomas Peyrin, editors, Advances in Cryptology - ASIACRYPT 2017, pages 380-409, Cham, 2017. Springer International Publishing.
Rafael Pass and Elaine Shi. Rethinking large-scale consensus. Cryptology ePrint Archive, Report 2018/302, 2018. URL: https://eprint.iacr.org/2018/302.
https://eprint.iacr.org/2018/302
Adi Shamir. How to share a secret. Commun. ACM, 22(11):612-613, 1979. URL: http://dx.doi.org/10.1145/359168.359176.
http://dx.doi.org/10.1145/359168.359176
Yoav Shoham and Moshe Tennenholtz. Non-cooperative computation: Boolean functions with correctness and exclusivity. Theoretical Computer Science, 343(1–2):97-113, 2005.
Márió Szegedy and Sundar Vishwanathan. Locality based graph coloring. In Proceedings of the Twenty-fifth Annual ACM Symposium on Theory of Computing, STOC '93, pages 201-207, New York, NY, USA, 1993. ACM. URL: http://dx.doi.org/10.1145/167088.167156.
http://dx.doi.org/10.1145/167088.167156
Amparo Urbano and Jose E. Vila. Computational complexity and communication: Coordination in two-player games. Econometrica, 70(5):1893-1927, September 2002. URL: http://ideas.repec.org/a/ecm/emetrp/v70y2002i5p1893-1927.html.
http://ideas.repec.org/a/ecm/emetrp/v70y2002i5p1893-1927.html
Amparo Urbano and José E. Vila. Computationally restricted unmediated talk under incomplete information. Economic theory, 2004.
Edmund L. Wong, Isaac Levy, Lorenzo Alvisi, Allen Clement, and Michael Dahlin. Regret freedom isn't free. In OPODIS, pages 80-95, 2011. URL: http://dx.doi.org/10.1007/978-3-642-25873-2_7.
http://dx.doi.org/10.1007/978-3-642-25873-2_7
Assaf Yifrach and Yishay Mansour. Fair leader election for rational agents in asynchronous rings and networks. In PODC '18, 2018. URL: http://dx.doi.org/10.1145/3212734.3212767.
http://dx.doi.org/10.1145/3212734.3212767
Yehuda Afek, Shaked Rafaeli, and Moshe Sulamy
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Distributed Approximate Maximum Matching in the CONGEST Model
We study distributed algorithms for the maximum matching problem in the CONGEST model, where each message must be bounded in size. We give new deterministic upper bounds, and a new lower bound on the problem.
We begin by giving a distributed algorithm that computes an exact maximum (unweighted) matching in bipartite graphs, in O(n log n) rounds. Next, we give a distributed algorithm that approximates the fractional weighted maximum matching problem in general graphs. In a graph with maximum degree at most Delta, the algorithm computes a (1-epsilon)-approximation for the problem in time O(log(Delta W)/epsilon^2), where W is a bound on the ratio between the largest and the smallest edge weight. Next, we show a slightly improved and generalized version of the deterministic rounding algorithm of Fischer [DISC '17]. Given a fractional weighted maximum matching solution of value f for a given graph G, we show that in time O((log^2(Delta)+log^*n)/epsilon), the fractional solution can be turned into an integer solution of value at least (1-epsilon)f for bipartite graphs and (1-epsilon) * (g-1)/g * f for general graphs, where g is the length of the shortest odd cycle of G. Together with the above fractional maximum matching algorithm, this implies a deterministic algorithm that computes a (1-epsilon)* (g-1)/g-approximation for the weighted maximum matching problem in time O(log(Delta W)/epsilon^2 + (log^2(Delta)+log^* n)/epsilon).
On the lower-bound front, we show that even for unweighted fractional maximum matching in bipartite graphs, computing an (1 - O(1/sqrt{n}))-approximate solution requires at least Omega~(D+sqrt{n}) rounds in CONGEST. This lower bound requires the introduction of a new 2-party communication problem, for which we prove a tight lower bound.
distributed graph algorithms
maximum matching
deterministic rounding
communication complexity
Mathematics of computing~Graph algorithms
Mathematics of computing~Approximation algorithms
6:1-6:17
Regular Paper
A full version of the paper is available at [M. Ahmadi et al., 2018], http://tr.informatik.uni-freiburg.de/reports/report286/report00286.pdf.
Mohamad
Ahmadi
Mohamad Ahmadi
University of Freiburg, Germany
Supported by ERC Grant No. 336495 (ACDC).
Fabian
Kuhn
Fabian Kuhn
University of Freiburg, Germany
Supported by ERC Grant No. 336495 (ACDC).
Rotem
Oshman
Rotem Oshman
Tel Aviv University, Israel
10.4230/LIPIcs.DISC.2018.6
M. Ahmadi, F. Kuhn, and R. Oshman. Distributed approximate maximum matching in the congest model. Technical Report 286, U. Freiburg, Dept. of Computer Science, 2018. URL: http://tr.informatik.uni-freiburg.de/reports/report286/report00286.pdf.
http://tr.informatik.uni-freiburg.de/reports/report286/report00286.pdf
N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7(4):567-583, 1986.
R. Bar-Yehuda, K. Censor-Hillel, M. Ghaffari, and G. Schwartzman. Distributed approximation of maximum independent set and maximum matching. In Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC), pages 165-174, 2017.
Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. An information statistics approach to data stream and communication complexity. J. Comput. Syst. Sci., 68(4):702-732, 2004.
L. Barenboim, M. Elkin, S. Pettie, and J. Schneider. The locality of distributed symmetry breaking. In Proceedings of 53th Symposium on Foundations of Computer Science (FOCS), 2012.
A. Czygrinow and M. Hańćkowiak. Distributed algorithm for better approximation of the maximum matching. In 9th Annual International Computing and Combinatorics Conference (COCOON), pages 242-251, 2003.
J. Edmonds. Maximum matching and a polyhedron with 0,1 vertices. Canadian Journal of mathematics, pages 449-467, 1965.
J. Edmonds. Paths, trees, and flowers. J. of Res. the Nat. Bureau of Standards, 69 B:125-130, 1965.
F. Eisenbrand, S. Funke, N. Garg, and J. Könemann. A combinatorial algorithm for computing a maximum independent set in a t-perfect graph. In Proceedings of 14th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 517-522, 2003.
G. Even, M. Medina, and D. Ron. Distributed maximum matching in bounded degree graphs. In Proceedings of the 2015 International Conference on Distributed Computing and Networking (ICDCN), pages 18:1-18:10, 2015.
M. Fischer. Improved deterministic distributed matching via rounding. In Proceedings of 31st Symposium on Distributed Computing (DISC), pages 17:1-17:15, 2017.
M. Fischer, M. Ghaffari, and F. Kuhn. Deterministic distributed edge-coloring via hypergraph maximal matching. In Proceedings of 58th IEEE Annual Symposium on Foundations of Computer Science (FOCS), pages 180-191, 2017.
M. Ghaffari, D. G. Harris, and F. Kuhn. On derandomizing local distributed algorithms, 2017. URL: http://arxiv.org/abs/1711.02194.
http://arxiv.org/abs/1711.02194
M. Hańćkowiak, M. Karoński, and A. Panconesi. On the distributed complexity of computing maximal matchings. In Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 219-225, 1998.
M. Hańćkowiak, M. Karoński, and A. Panconesi. A faster distributed algorithm for computing maximal matchings deterministically. In Proceedings of the Eighteenth Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 219-228, 1999.
A. Israeli and Y. Shiloach. An improved parallel algorithm for maximal matching. Inf. Process. Lett., 22(2):57-60, 1986.
R. M. Karp and J. E. Hopcroft. An n^5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing, 1973.
F. Kuhn and T. Moscibroda. Distributed approximation of capacitated dominating sets. In Proceedings of 19th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 161-170, 2007.
F. Kuhn, T. Moscibroda, and R. Wattenhofer. The price of being near-sighted. In Proceedings of 17th Symposium on Discrete Algorithms (SODA), pages 980-989, 2006.
F. Kuhn, T. Moscibroda, and R. Wattenhofer. Local computation: Lower and upper bounds. J. of the ACM, 63(2), 2016.
Z. Lotker, B. Patt-Shamir, and S. Pettie. Improved distributed approximate matching. In Proceedings of the 20th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 129-136, 2008.
Z. Lotker, B. Patt-Shamir, and A. Rosén. Distributed approximate matching. SIAM Journal on Computing, 39(2):445-460, 2009.
M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM Journal on Computing, 15:1036-1053, 1986.
Andrew McGregor. Finding graph matchings in data streams. In Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques, pages 170-181, 2005.
D. Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM, 2000.
S. Plotkin, D. Shmoys, and E. Tardos. Fast approximation algorithms for fractional packing and covering problems. Mathematics of Operations Research, 20:257-301, 1995.
Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. SIAM J. Comput., 41(5):1235-1265, 2012.
M. Wattenhofer and R. Wattenhofer. Distributed weighted matching. In Proceedings of 18th International Distributed Computing Conference (DISC), pages 335-348, 2004.
Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. An improved constant-time approximation algorithm for maximum matchings. In STOC '09, pages 225-234, 2009.
Mohamad Ahmadi, Fabian Kuhn, and Rotem Oshman
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
State Machine Replication Is More Expensive Than Consensus
Consensus and State Machine Replication (SMR) are generally considered to be equivalent problems. In certain system models, indeed, the two problems are computationally equivalent: any solution to the former problem leads to a solution to the latter, and vice versa.
In this paper, we study the relation between consensus and SMR from a complexity perspective. We find that, surprisingly, completing an SMR command can be more expensive than solving a consensus instance. Specifically, given a synchronous system model where every instance of consensus always terminates in constant time, completing an SMR command does not necessarily terminate in constant time. This result naturally extends to partially synchronous models. Besides theoretical interest, our result also corresponds to practical phenomena we identify empirically. We experiment with two well-known SMR implementations (Multi-Paxos and Raft) and show that, indeed, SMR is more expensive than consensus in practice. One important implication of our result is that - even under synchrony conditions - no SMR algorithm can ensure bounded response times.
Consensus
State machine replication
Synchronous model
Computing methodologies~Distributed algorithms
7:1-7:18
Regular Paper
https://infoscience.epfl.ch/record/256238
Karolos
Antoniadis
Karolos Antoniadis
EPFL, Lausanne, Switzerland
Rachid
Guerraoui
Rachid Guerraoui
EPFL, Lausanne, Switzerland
Dahlia
Malkhi
Dahlia Malkhi
VMware Research, Palo Alto, USA
Dragos-Adrian
Seredinschi
Dragos-Adrian Seredinschi
EPFL, Lausanne, Switzerland
10.4230/LIPIcs.DISC.2018.7
Amazon EC2. http://aws.amazon.com/ec2/. [Online; accessed 9-May-2018].
http://aws.amazon.com/ec2/
etcd. https://github.com/coreos/etcd. [Online; accessed 9-May-2018].
https://github.com/coreos/etcd
LibPaxos3. https://bitbucket.org/sciascid/libpaxos. [Online; accessed 9-May-2018].
https://bitbucket.org/sciascid/libpaxos
Karolos Antoniadis, Rachid Guerraoui, Dahlia Malkhi, and Dragos-Adrian Seredinschi. State Machine Replication is More Expensive Than Consensus. Technical Report 256238, EPFL, 2018. URL: https://infoscience.epfl.ch/record/256238.
https://infoscience.epfl.ch/record/256238
B. Arun, S. Peluso, R. Palmieri, G. Losa, and B. Ravindran. Speeding up Consensus by Chasing Fast Decisions. In DSN, 2017.
Peter Bailis and Kyle Kingsbury. The network is reliable. ACM Queue, 12(7):20, 2014.
Alysson Bessani, Marcel Santos, João Felix, Nuno Neves, and Miguel Correia. On the efficiency of durable state machine replication. In ATC, 2013.
Alysson Bessani, João Sousa, and Eduardo EP Alchieri. State machine replication for the masses with bft-smart. In DSN, 2014.
Martin Biely, Peter Robinson, Ulrich Schmid, Manfred Schwarz, and Kyrill Winkler. Gracefully degrading consensus and k-set agreement in directed dynamic networks. Theoretical Computer Science, 726:41-77, 2018.
Christian Cachin, Rachid Guerraoui, and Luìs Rodrigues. Introduction to Reliable and Secure Distributed Programming. Springer, 2011.
Lásaro Jonas Camargos, Rodrigo Malta Schmidt, and Fernando Pedone. Multicoordinated agreement protocols for higher availability. In Network Computing and Applications, 2008.
Daniel Cason, Parisa J Marandi, Luiz E Buzato, and Fernando Pedone. Chasing the tail of atomic broadcast protocols. In SRDS, 2015.
Tushar D. Chandra, Robert Griesemer, and Joshua Redstone. Paxos made live: An engineering perspective. In PODC, 2007.
Tushar D. Chandra and Sam Toueg. Unreliable failure detectors for reliable distributed systems. Journal of the ACM (JACM), 43(2):225-267, 1996.
Bernadette Charron-Bost and André Schiper. The heard-of model: computing in distributed systems with benign faults. Distributed Computing, 22(1):49-71, Apr 2009.
James C. Corbett, Jeffrey Dean, Michael Epstein, Andrew Fikes, Christopher Frost, J. J. Furman, Sanjay Ghemawat, Andrey Gubarev, Christopher Heiser, Peter Hochschild, Wilson Hsieh, Sebastian Kanthak, Eugene Kogan, Hongyi Li, Alexander Lloyd, Sergey Melnik, David Mwaura, David Nagle, Sean Quinlan, Rajesh Rao, Lindsay Rolig, Yasushi Saito, Michal Szymaniak, Christopher Taylor, Ruth Wang, and Dale Woodford. Spanner: Google’s globally distributed database. ACM TOCS, 31(3):8:1-8:22, 2013.
Jeffrey Dean and Luiz André Barroso. The tail at scale. Communications of the ACM, 56(2):74-80, 2013.
Tzilla Elrad and Nissim Francez. Decomposition of distributed programs into communication-closed layers. Science of Computer Programming, 2(3):155-173, 1982.
Michael J Fischer, Nancy A Lynch, and Michael S Paterson. Impossibility of distributed consensus with one faulty process. Journal of the ACM (JACM), 32(2):374-382, 1985.
Eli Gafni. Round-by-round fault detectors (extended abstract): Unifying synchrony and asynchrony. In PODC, 1998.
Álvaro García-Pérez, Alexey Gotsman, Yuri Meshman, and Ilya Sergey. Paxos consensus, deconstructed and abstracted (extended version). CoRR, abs/1802.05969, 2018.
Chryssis Georgiou, Seth Gilbert, Rachid Guerraoui, and Dariusz R. Kowalski. On the complexity of asynchronous gossip. In PODC, 2008.
Sanjay Ghemawat, Howard Gobioff, and Shun-Tak Leung. The Google File System. In SOSP, 2003.
Rachid Guerraoui, Matej Pavlovic, and Dragos-Adrian Seredinschi. Incremental consistency guarantees for replicated objects. In OSDI, 2016.
Heidi Howard and Jon Crowcroft. Coracle: Evaluating Consensus at the Internet Edge. In SIGCOMM, 2015.
Heidi Howard, Dahlia Malkhi, and Alexander Spiegelman. Flexible Paxos: Quorum Intersection Revisited. In OPODIS, 2016.
Patrick Hunt, Mahadev Konar, Flavio Paiva Junqueira, and Benjamin Reed. Zookeeper: Wait-free coordination for internet-scale systems. In USENIX ATC, 2010.
Idit Keidar and Sergio Rajsbaum. On the cost of fault-tolerant consensus when there are no faults: Preliminary version. SIGACT News, 32(2):45-63, 2001.
M. Kleppmann. Designing Data-Intensive Applications: The Big Ideas Behind Reliable, Scalable, and Maintainable Systems. O'Reilly Media, 2017.
Tim Kraska, Gene Pang, Michael J Franklin, Samuel Madden, and Alan Fekete. MDCC: Multi-data center consistency. In EuroSys, 2013.
Leslie Lamport. Time, Clocks, and the Ordering of Events in a Distributed System. Commun. ACM, 21(7):558-565, 1978.
Leslie Lamport. The part-time parliament. ACM TOCS, 16(2):133-169, 1998.
Leslie Lamport. Paxos made simple. ACM Sigact News, 32(4):18-25, 2001.
Leslie Lamport. Lower bounds for asynchronous consensus. In Future Directions in Distributed Computing, pages 22-23. Springer, 2003.
Leslie Lamport. Fast paxos. Distributed Computing, 19(2):79-103, 2006.
Leslie Lamport, Dahlia Malkhi, and Lidong Zhou. Stoppable Paxos. TechReport, Microsoft Research, 2008.
Leslie Lamport and Mike Massa. Cheap paxos. In DSN, 2004.
Barbara Liskov, Sanjay Ghemawat, Robert Gruber, Paul Johnson, Liuba Shrira, and Michael Williams. Replication in the Harp File System. In SOSP, 1991.
John MacCormick, Nick Murphy, Marc Najork, Chandu Thekkath, and Lidong Zhou. Boxwood: Abstractions as the foundation for storage infrastructure. In OSDI, 2004.
Iulian Moraru, David G. Andersen, and Michael Kaminsky. There is More Consensus in Egalitarian Parliaments. In SOSP, 2013.
Yoram Moses and Sergio Rajsbaum. A layered analysis of consensus. SIAM Journal on Computing, 31(4):989-1021, 2002.
A. Mostefaoui and M. Raynal. Low cost consensus-based atomic broadcast. In Proceedings. 2000 Pacific Rim International Symposium on Dependable Computing, 2000.
Diego Ongaro and John Ousterhout. In search of an understandable consensus algorithm. In ATC, 2014.
Nicola Santoro and Peter Widmayer. Time is not a healer. In STACS, 1989.
Nicola Santoro and Peter Widmayer. Agreement in synchronous networks with ubiquitous faults. Theoretical Computer Science, 384(2):232-249, 2007.
Nuno Santos and André Schiper. Tuning paxos for high-throughput with batching and pipelining. In International Conference on Distributed Computing and Networking, pages 153-167. Springer, 2012.
Ulrich Schmid, Bettina Weiss, and Idit Keidar. Impossibility results and lower bounds for consensus under link failures. SIAM Journal on Computing, 38(5):1912-1951, 2009.
Ulrich Schmid, Bettina Weiss, and John Rushby. Formally verified byzantine agreement in presence of link faults. In ICDCS, 2002.
Fred B. Schneider. Implementing fault-tolerant services using the state machine approach: A tutorial. ACM Comput. Surv., 22(4):299-319, 1990.
Emil Sit, Andreas Haeberlen, Frank Dabek, Byung-Gon Chun, Hakim Weatherspoon, Robert Morris, M Frans Kaashoek, and John Kubiatowicz. Proactive Replication for Data Durability. In IPTPS, 2006.
Robert H Thomas. A majority consensus approach to concurrency control for multiple copy databases. ACM TODS, 4(2):180-209, 1979.
Gustavo M. D. Vieira, Islene C. Garcia, and Luiz Eduardo Buzato. Seamless paxos coordinators. CoRR, abs/1710.07845, 2017. URL: http://arxiv.org/abs/1710.07845.
http://arxiv.org/abs/1710.07845
Matt Welsh, David Culler, and Eric Brewer. Seda: An architecture for well-conditioned, scalable internet services. In SOSP, 2001.
Benjamin Wester, James A Cowling, Edmund B Nightingale, Peter M Chen, Jason Flinn, and Barbara Liskov. Tolerating latency in replicated state machines through client speculation. In NSDI, 2009.
Karolos Antoniadis, Rachid Guerraoui, Dahlia Malkhi, and Dragos-Adrian Seredinschi
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Allocate-On-Use Space Complexity of Shared-Memory Algorithms
Many fundamental problems in shared-memory distributed computing, including mutual exclusion [James E. Burns and Nancy A. Lynch, 1993], consensus [Leqi Zhu, 2016], and implementations of many sequential objects [Prasad Jayanti et al., 2000], are known to require linear space in the worst case. However, these lower bounds all work by constructing particular executions for any given algorithm that may be both very long and very improbable. The significance of these bounds is justified by an assumption that any space that is used in some execution must be allocated for all executions. This assumption is not consistent with the storage allocation mechanisms of actual practical systems.
We consider the consequences of adopting a per-execution approach to space complexity, where an object only counts toward the space complexity of an execution if it is used in that execution. This allows us to show that many known randomized algorithms for fundamental problems in shared-memory distributed computing have expected space complexity much lower than the worst-case lower bounds, and that many algorithms that are adaptive in time complexity can also be made adaptive in space complexity.
For the specific problem of mutual exclusion, we develop a new algorithm that illustrates an apparent trade-off between low expected space complexity and low expected RMR complexity. Whether this trade-off is necessary is an open problem.
For some applications, it may be helpful to pay only for objects that are updated, as opposed to those that are merely read. We give a data structure that requires no space to represent objects that are not updated at the cost of a small overhead on those that are.
Space complexity
memory allocation
mutual exclusion
Theory of computation~Distributed computing models
Computing methodologies~Shared memory algorithms
Software and its engineering~Mutual exclusion
8:1-8:17
Regular Paper
James
Aspnes
James Aspnes
Yale University Department of Computer Science, New Haven, CT, USA
Supported in part by NSF grants CCF-1637385 and CCF-1650596.
Bernhard
Haeupler
Bernhard Haeupler
Carnegie Mellon School of Computer Science, Pittsburgh, PA, USA
Alexander
Tong
Alexander Tong
Yale University Department of Computer Science, New Haven, CT, USA
Supported by NSF grant CCF-1650596.
Philipp
Woelfel
Philipp Woelfel
University of Calgary, Department of Computer Science, Calgary, AB, Canada
10.4230/LIPIcs.DISC.2018.8
Dan Alistarh and James Aspnes. Sub-logarithmic test-and-set against a weak adversary. In Distributed Computing: 25th International Symposium, DISC 2011, volume 6950 of Lecture Notes in Computer Science, pages 97-109. Springer-Verlag, 2011.
Dan Alistarh, Hagit Attiya, Seth Gilbert, Andrei Giurgiu, and Rachid Guerraoui. Fast randomized test-and-set and renaming. In Nancy A. Lynch and Alexander A. Shvartsman, editors, Distributed Computing, 24th International Symposium, DISC 2010, Cambridge, MA, USA, September 13-15, 2010. Proceedings, volume 6343 of Lecture Notes in Computer Science, pages 94-108. Springer, 2010. URL: http://dx.doi.org/10.1007/978-3-642-15763-9_9.
http://dx.doi.org/10.1007/978-3-642-15763-9_9
James Aspnes. Faster randomized consensus with an oblivious adversary. In 2012 ACM Symposium on Principles of Distributed Computing, pages 1-8, 2012.
James Aspnes and Faith Ellen. Tight bounds for adopt-commit objects. Theory of Computing Systems, 55(3):451-474, 2014. URL: http://dx.doi.org/10.1007/s00224-013-9448-1.
http://dx.doi.org/10.1007/s00224-013-9448-1
Hagit Attiya, Danny Hendler, and Philipp Woelfel. Tight RMR lower bounds for mutual exclusion and other problems. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, May 17-20, 2008, pages 217-226, 2008. URL: http://dx.doi.org/10.1145/1374376.1374410.
http://dx.doi.org/10.1145/1374376.1374410
Hagit Attiya, Fabian Kuhn, C. Greg Plaxton, Mirjam Wattenhofer, and Roger Wattenhofer. Efficient adaptive collect using randomization. Distributed Computing, 18(3):179-188, 2006. URL: http://dx.doi.org/10.1007/s00446-005-0143-6.
http://dx.doi.org/10.1007/s00446-005-0143-6
Michael A. Bender and Seth Gilbert. Mutual exclusion with o(log^2 log n) amortized work. In Rafail Ostrovsky, editor, IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, Palm Springs, CA, USA, October 22-25, 2011, pages 728-737. IEEE Computer Society, 2011. URL: http://dx.doi.org/10.1109/FOCS.2011.84.
http://dx.doi.org/10.1109/FOCS.2011.84
James E. Burns and Nancy A. Lynch. Bounds on shared memory for mutual exclusion. Inf. Comput., 107(2):171-184, 1993. URL: http://dx.doi.org/10.1006/inco.1993.1065.
http://dx.doi.org/10.1006/inco.1993.1065
P. Elias. Universal codeword sets and representations of the integers. IEEE Transactions on Information Theory, 21(2):194-203, March 1975. URL: http://dx.doi.org/10.1109/TIT.1975.1055349.
http://dx.doi.org/10.1109/TIT.1975.1055349
Rati Gelashvili. On the optimal space complexity of consensus for anonymous processes. In Yoram Moses, editor, Distributed Computing: 29th International Symposium, DISC 2015, Tokyo, Japan, October 7-9, 2015, Proceedings, pages 452-466, Berlin, Heidelberg, 2015. Springer Berlin Heidelberg. URL: http://dx.doi.org/10.1007/978-3-662-48653-5_30.
http://dx.doi.org/10.1007/978-3-662-48653-5_30
George Giakkoupis and Philipp Woelfel. On the time and space complexity of randomized test-and-set. In Darek Kowalski and Alessandro Panconesi, editors, ACM Symposium on Principles of Distributed Computing, PODC '12, Funchal, Madeira, Portugal, July 16-18, 2012, pages 19-28. ACM, 2012. URL: http://dx.doi.org/10.1145/2332432.2332436.
http://dx.doi.org/10.1145/2332432.2332436
George Giakkoupis and Philipp Woelfel. Randomized abortable mutual exclusion with constant amortized RMR complexity on the CC model. In Elad Michael Schiller and Alexander A. Schwarzmann, editors, Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2017, Washington, DC, USA, July 25-27, 2017, pages 221-229. ACM, 2017. URL: http://dx.doi.org/10.1145/3087801.3087837.
http://dx.doi.org/10.1145/3087801.3087837
Danny Hendler and Philipp Woelfel. Randomized mutual exclusion with sub-logarithmic rmr-complexity. Distributed Computing, 24(1):3-19, 2011. URL: http://dx.doi.org/10.1007/s00446-011-0128-6.
http://dx.doi.org/10.1007/s00446-011-0128-6
Prasad Jayanti, King Tan, and Sam Toueg. Time and space lower bounds for nonblocking implementations. SIAM J. Comput., 30(2):438-456, 2000. URL: http://dx.doi.org/10.1137/S0097539797317299.
http://dx.doi.org/10.1137/S0097539797317299
Leslie Lamport. A fast mutual exclusion algorithm. ACM Trans. Comput. Syst., 5(1):1-11, 1987. URL: http://dx.doi.org/10.1145/7351.7352.
http://dx.doi.org/10.1145/7351.7352
Mark Moir and James H. Anderson. Wait-free algorithms for fast, long-lived renaming. Sci. Comput. Program., 25(1):1-39, 1995.
Jae-Heon Yang and James H. Anderson. A fast, scalable mutual exclusion algorithm. Distributed Computing, 9(1):51-60, 1995. URL: http://dx.doi.org/10.1007/BF01784242.
http://dx.doi.org/10.1007/BF01784242
Leqi Zhu. A tight space bound for consensus. In Daniel Wichs and Yishay Mansour, editors, Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, Cambridge, MA, USA, June 18-21, 2016, pages 345-350. ACM, 2016. URL: http://dx.doi.org/10.1145/2897518.2897565.
http://dx.doi.org/10.1145/2897518.2897565
James Aspnes, Bernhard Haeupler, Alexander Tong, and Philipp Woelfel
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Almost Global Problems in the LOCAL Model
The landscape of the distributed time complexity is nowadays well-understood for subpolynomial complexities. When we look at deterministic algorithms in the LOCAL model and locally checkable problems (LCLs) in bounded-degree graphs, the following picture emerges:
- There are lots of problems with time complexities Theta(log^* n) or Theta(log n).
- It is not possible to have a problem with complexity between omega(log^* n) and o(log n).
- In general graphs, we can construct LCL problems with infinitely many complexities between omega(log n) and n^{o(1)}.
- In trees, problems with such complexities do not exist.
However, the high end of the complexity spectrum was left open by prior work. In general graphs there are problems with complexities of the form Theta(n^alpha) for any rational 0 < alpha <=1/2, while for trees only complexities of the form Theta(n^{1/k}) are known. No LCL problem with complexity between omega(sqrt{n}) and o(n) is known, and neither are there results that would show that such problems do not exist. We show that:
- In general graphs, we can construct LCL problems with infinitely many complexities between omega(sqrt{n}) and o(n).
- In trees, problems with such complexities do not exist.
Put otherwise, we show that any LCL with a complexity o(n) can be solved in time O(sqrt{n}) in trees, while the same is not true in general graphs.
Distributed complexity theory
locally checkable labellings
LOCAL model
Theory of computation~Distributed computing models
Theory of computation~Complexity classes
9:1-9:16
Regular Paper
This work was supported in part by the Academy of Finland, Grant 285721.
https://arxiv.org/pdf/1805.04776.pdf
Alkida
Balliu
Alkida Balliu
Aalto University, Finland
Sebastian
Brandt
Sebastian Brandt
ETH Zürich, Switzerland
Dennis
Olivetti
Dennis Olivetti
Aalto University, Finland
Jukka
Suomela
Jukka Suomela
Aalto University, Finland
10.4230/LIPIcs.DISC.2018.9
Alkida Balliu, Juho Hirvonen, Janne H. Korhonen, Tuomo Lempiäinen, Dennis Olivetti, and Jukka Suomela. New classes of distributed time complexity. In Proc. 50th Annual Symposium on the Theory of Computing (STOC 2018). ACM, 2018 (to appear). URL: http://arxiv.org/abs/1711.01871.
http://arxiv.org/abs/1711.01871
Leonid Barenboim. Deterministic (Δ + 1)-coloring in sublinear (in Δ) time in static, dynamic, and faulty networks. Journal of the ACM, 63(5):47:1-47:22, 2016. URL: http://dx.doi.org/10.1145/2979675.
http://dx.doi.org/10.1145/2979675
Leonid Barenboim, Michael Elkin, and Fabian Kuhn. Distributed (Δ+1)-coloring in linear (in Δ) time. SIAM Journal on Computing, 43(1):72-95, 2014. URL: http://dx.doi.org/10.1137/12088848X.
http://dx.doi.org/10.1137/12088848X
Sebastian Brandt, Orr Fischer, Juho Hirvonen, Barbara Keller, Tuomo Lempiäinen, Joel Rybicki, Jukka Suomela, and Jara Uitto. A lower bound for the distributed Lovász local lemma. In Proc. 48th Annual Symposium on the Theory of Computing (STOC 2016), pages 479-488. ACM, 2016. URL: http://dx.doi.org/10.1145/2897518.2897570.
http://dx.doi.org/10.1145/2897518.2897570
Sebastian Brandt, Juho Hirvonen, Janne H. Korhonen, Tuomo Lempiäinen, Patric R.J. Östergård, Christopher Purcell, Joel Rybicki, Jukka Suomela, and Przemysław Uznański. LCL problems on grids. In Proc. 35th ACM Symposium on the Principles of Distributed Computing (PODC 2017), pages 101-110, 2017. URL: http://dx.doi.org/10.1145/3087801.3087833.
http://dx.doi.org/10.1145/3087801.3087833
Yi-Jun Chang, Qizheng He, Wenzheng Li, Seth Pettie, and Jara Uitto. The complexity of distributed edge colouring with small palettes. In Proc. 29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018). Society for Industrial and Applied Mathematics, 2018.
Yi-Jun Chang, Tsvi Kopelowitz, and Seth Pettie. An exponential separation between randomized and deterministic complexity in the LOCAL model. In Proc. 57th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2016), pages 615-624. IEEE, 2016. URL: http://arxiv.org/abs/1602.08166.
http://arxiv.org/abs/1602.08166
Yi-Jun Chang and Seth Pettie. A time hierarchy theorem for the LOCAL model. In Proc. 58th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2017), 2017. URL: http://arxiv.org/abs/1704.06297.
http://arxiv.org/abs/1704.06297
Richard Cole and Uzi Vishkin. Deterministic coin tossing with applications to optimal parallel list ranking. Information and Control, 70(1):32-53, 1986. URL: http://dx.doi.org/10.1016/S0019-9958(86)80023-7.
http://dx.doi.org/10.1016/S0019-9958(86)80023-7
Pierre Fraigniaud, Marc Heinrich, and Adrian Kosowski. Local conflict coloring. In Proc. 57th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2016), pages 625-634, 2016. URL: http://dx.doi.org/10.1109/FOCS.2016.73.
http://dx.doi.org/10.1109/FOCS.2016.73
Mohsen Ghaffari and Hsin-Hao Su. Distributed degree splitting, edge coloring, and orientations. In Proc. 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), pages 2505-2523. Society for Industrial and Applied Mathematics, 2017. URL: http://dx.doi.org/10.1137/1.9781611974782.166.
http://dx.doi.org/10.1137/1.9781611974782.166
Juris Hartmanis and Richard Edwin Stearns. On the computational complexity of algorithms. Transactions of the American Mathematical Society, 117:285-306, 1965. URL: http://dx.doi.org/10.1090/S0002-9947-1965-0170805-7.
http://dx.doi.org/10.1090/S0002-9947-1965-0170805-7
John E. Hopcroft and Jeffrey D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.
Nathan Linial. Locality in distributed graph algorithms. SIAM Journal on Computing, 21(1):193-201, 1992. URL: http://dx.doi.org/10.1137/0221015.
http://dx.doi.org/10.1137/0221015
Moni Naor and Larry Stockmeyer. What can be computed locally? SIAM Journal on Computing, 24(6):1259-1277, 1995. URL: http://dx.doi.org/10.1137/S0097539793254571.
http://dx.doi.org/10.1137/S0097539793254571
Alessandro Panconesi and Romeo Rizzi. Some simple distributed algorithms for sparse networks. Distributed Computing, 14(2):97-100, 2001. URL: http://dx.doi.org/10.1007/PL00008932.
http://dx.doi.org/10.1007/PL00008932
Alessandro Panconesi and Aravind Srinivasan. The local nature of Δ-coloring and its algorithmic applications. Combinatorica, 15(2):255-280, 1995. URL: http://dx.doi.org/10.1007/BF01200759.
http://dx.doi.org/10.1007/BF01200759
David Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia, 2000.
Alkida Balliu, Sebastian Brandt, Dennis Olivetti, and Jukka Suomela
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
A Population Protocol for Exact Majority with O(log5/3 n) Stabilization Time and Theta(log n) States
A population protocol is a sequence of pairwise interactions of n agents. During one interaction, two randomly selected agents update their states by applying a deterministic transition function. The goal is to stabilize the system at a desired output property. The main performance objectives in designing such protocols are small number of states per agent and fast stabilization time.
We present a fast population protocol for the exact-majority problem, which uses Theta(log n) states (per agent) and stabilizes in O(log^{5/3} n) parallel time (i.e., in O(n log^{5/3} n) interactions) in expectation and with high probability. Alistarh et al. [SODA 2018] showed that exact-majority protocols which stabilize in expected O(n^{1-Omega(1)}) parallel time and have the properties of monotonicity and output dominance require Omega(log n) states. Note that the properties mentioned above are satisfied by all known population protocols for exact majority, including ours. They also showed an O(log^2 n)-time exact-majority protocol with O(log n) states, which, prior to our work, was the fastest exact-majority protocol with polylogarithmic number of states. The standard design framework for majority protocols is based on O(log n) phases and requires that all agents are well synchronized within each phase, leading naturally to upper bounds of the order of log^2 n because of Theta(log n) synchronization time per phase. We show how this framework can be tightened with weak synchronization to break the O(log^2 n) upper bound of previous protocols.
Population Protocols
Randomized Algorithms
Majority
Theory of computation~Distributed computing models
10:1-10:18
Regular Paper
https://arxiv.org/abs/1805.05157
Petra
Berenbrink
Petra Berenbrink
Universität Hamburg, Hamburg, Germany
Robert
Elsässer
Robert Elsässer
University of Salzburg, Salzburg, Austria
https://orcid.org/0000-0002-5766-8103
Robert Elsässer’s work has been supported by grant no. P 27613 of the Austrian Science Fund (FWF), "Distributed Voting in Large Networks".
Tom
Friedetzky
Tom Friedetzky
Durham University, Durham, U.K.
https://orcid.org/0000-0002-1299-5514
Dominik
Kaaser
Dominik Kaaser
Universität Hamburg, Hamburg, Germany
https://orcid.org/0000-0002-2083-7145
Peter
Kling
Peter Kling
Universität Hamburg, Hamburg, Germany
https://orcid.org/0000-0003-0000-8689
Tomasz
Radzik
Tomasz Radzik
King’s College London, London, U.K.
https://orcid.org/0000-0002-7776-5461
Tomasz Radzik’s work has been supported by EPSRC grant EP/M005038/1, "Randomized algorithms for computer networks".
10.4230/LIPIcs.DISC.2018.10
Dan Alistarh, James Aspnes, David Eisenstat, Rati Gelashvili, and Ronald L. Rivest. Time-space trade-offs in population protocols. In Philip N. Klein, editor, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 2560-2579. SIAM, 2017. URL: http://dx.doi.org/10.1137/1.9781611974782.169.
http://dx.doi.org/10.1137/1.9781611974782.169
Dan Alistarh, James Aspnes, and Rati Gelashvili. Space-optimal majority in population protocols. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, January 7-10, 2018, pages 2221-2239, 2018. URL: http://dx.doi.org/10.1137/1.9781611975031.144.
http://dx.doi.org/10.1137/1.9781611975031.144
Dan Alistarh, Rati Gelashvili, and Milan Vojnovic. Fast and exact majority in population protocols. In Chryssis Georgiou and Paul G. Spirakis, editors, Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC 2015, Donostia-San Sebastián, Spain, July 21 - 23, 2015, pages 47-56. ACM, 2015. URL: http://dl.acm.org/citation.cfm?id=2767386, URL: http://dx.doi.org/10.1145/2767386.2767429.
http://dx.doi.org/10.1145/2767386.2767429
Dana Angluin, James Aspnes, Zoë Diamadi, Michael J. Fischer, and René Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Computing, 18(4):235-253, 2006. URL: http://dx.doi.org/10.1007/s00446-005-0138-3.
http://dx.doi.org/10.1007/s00446-005-0138-3
Dana Angluin, James Aspnes, and David Eisenstat. Fast computation by population protocols with a leader. Distributed Computing, 21(3):183-199, 2008.
James Aspnes and Eric Ruppert. An introduction to population protocols. In Benoît Garbinato, Hugo Miranda, and Luís Rodrigues, editors, Middleware for Network Eccentric and Mobile Applications, pages 97-120. Springer-Verlag, 2009.
Florence Bénézit, Patrick Thiran, and Martin Vetterli. Interval consensus: From quantized gossip to voting. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, 19-24 April 2009, Taipei, Taiwan, pages 3661-3664. IEEE, 2009. URL: http://dx.doi.org/10.1109/ICASSP.2009.4960420.
http://dx.doi.org/10.1109/ICASSP.2009.4960420
Petra Berenbrink, Robert Elässser, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik. Majority &stabilization in population protocols. Unpublished manuscript, available on arXiv, May 2018.
Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik. A population protocol for exact majority with O(log^5/3 n) stabilization time and asymptotically optimal number of states. Unpublished manuscript, available on arXiv, May 2018. URL: http://arxiv.org/abs/1805.05157.
http://arxiv.org/abs/1805.05157
Petra Berenbrink, Tom Friedetzky, Peter Kling, Frederik Mallmann-Trenn, and Chris Wastell. Plurality consensus via shuffling: Lessons learned from load balancing. CoRR, abs/1602.01342, 2016. URL: http://arxiv.org/abs/1602.01342.
http://arxiv.org/abs/1602.01342
Andreas Bilke, Colin Cooper, Robert Elsässer, and Tomasz Radzik. Brief announcement: Population protocols for leader election and exact majority with O(log^2 n) states and O(log^2 n) convergence time. In Elad Michael Schiller and Alexander A. Schwarzmann, editors, Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2017, Washington, DC, USA, July 25-27, 2017, pages 451-453. ACM, 2017. Full version available at arXiv:1705.01146. URL: http://dx.doi.org/10.1145/3087801.3087858.
http://dx.doi.org/10.1145/3087801.3087858
Moez Draief and Milan Vojnovic. Convergence speed of binary interval consensus. In INFOCOM 2010. 29th IEEE International Conference on Computer Communications, Joint Conference of the IEEE Computer and Communications Societies, 15-19 March 2010, San Diego, CA, USA, pages 1792-1800. IEEE, 2010. URL: http://dx.doi.org/10.1109/INFCOM.2010.5461999.
http://dx.doi.org/10.1109/INFCOM.2010.5461999
Leszek Gasieniec and Grzegorz Stachowiak. Fast space optimal leader election in population protocols. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, January 7-10, 2018, pages 2653-2667, 2018. URL: http://dx.doi.org/10.1137/1.9781611975031.169.
http://dx.doi.org/10.1137/1.9781611975031.169
Leszek Gasieniec, Grzegorz Stachowiak, and Przemyslaw Uznanski. Almost logarithmic-time space optimal leader election in population protocols. CoRR, abs/1802.06867, 2018. URL: http://arxiv.org/abs/1802.06867.
http://arxiv.org/abs/1802.06867
Mohsen Ghaffari and Merav Parter. A polylogarithmic gossip algorithm for plurality consensus. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing PODC, pages 117-126, 2016.
A. Kosowski and P. Uznański. Population Protocols Are Fast. ArXiv e-prints, 2018. URL: http://arxiv.org/abs/1802.06872v2.
http://arxiv.org/abs/1802.06872v2
George B. Mertzios, Sotiris E. Nikoletseas, Christoforos L. Raptopoulos, and Paul G. Spirakis. Determining majority in networks with local interactions and very small local memory. In Javier Esparza, Pierre Fraigniaud, Thore Husfeldt, and Elias Koutsoupias, editors, Automata, Languages, and Programming, volume 8572 of Lecture Notes in Computer Science, pages 871-882. Springer Berlin Heidelberg, 2014. URL: http://dx.doi.org/10.1007/978-3-662-43948-7_72.
http://dx.doi.org/10.1007/978-3-662-43948-7_72
Thomas Sauerwald and He Sun. Tight bounds for randomized load balancing on arbitrary network topologies. In 53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012, New Brunswick, NJ, USA, October 20-23, 2012, pages 341-350. IEEE Computer Society, 2012. URL: http://dx.doi.org/10.1109/FOCS.2012.86.
http://dx.doi.org/10.1109/FOCS.2012.86
Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Integrated Bounds for Disintegrated Storage
We point out a somewhat surprising similarity between non-authenticated Byzantine storage, coded storage, and certain emulations of shared registers from smaller ones. A common characteristic in all of these is the inability of reads to safely return a value obtained in a single atomic access to shared storage. We collectively refer to such systems as disintegrated storage, and show integrated space lower bounds for asynchronous regular wait-free emulations in all of them. In a nutshell, if readers are invisible, then the storage cost of such systems is inherently exponential in the size of written values; otherwise, it is at least linear in the number of readers. Our bounds are asymptotically tight to known algorithms, and thus justify their high costs.
storage
coding
lower bounds
space complexity
register emulations
Theory of computation~Distributed computing models
Computing methodologies~Distributed algorithms
11:1-11:18
Regular Paper
Alon
Berger
Alon Berger
Viterbi Department of Electrical Engineering, Technion, Haifa, Israel
Idit
Keidar
Idit Keidar
Viterbi Department of Electrical Engineering, Technion, Haifa, Israel
Alexander
Spiegelman
Alexander Spiegelman
VMware Research, Israel
10.4230/LIPIcs.DISC.2018.11
Ittai Abraham, Gregory Chockler, Idit Keidar, and Dahlia Malkhi. Byzantine disk paxos: optimal resilience with byzantine shared memory. Distributed Computing, 18(5):387-408, 2006.
Ittai Abraham, Gregory Chockler, Idit Keidar, and Dahlia Malkhi. Wait-free regular storage from byzantine components. Information Processing Letters, 101(2):60-65, 2007.
Marcos K. Aguilera, Burkhard Englert, and Eli Gafni. On using network attached disks as shared memory. In Proceedings of the Twenty-second Annual Symposium on Principles of Distributed Computing, PODC '03, pages 315-324, New York, NY, USA, 2003. ACM. URL: http://dx.doi.org/10.1145/872035.872082.
http://dx.doi.org/10.1145/872035.872082
Marcos Kawazoe Aguilera, Ramaprabhu Janakiraman, and Lihao Xu. Using erasure codes efficiently for storage in a distributed system. In 2005 International Conference on Dependable Systems and Networks (DSN'05), pages 336-345, June 2005.
Elli Androulaki, Christian Cachin, Dan Dobre, and Marko Vukolić. Erasure-coded byzantine storage with separate metadata. In International Conference on Principles of Distributed Systems, pages 76-90. Springer, 2014.
Hagit Attiya, Amotz Bar-Noy, and Danny Dolev. Sharing memory robustly in message-passing systems. Journal of the ACM (JACM), 42(1):124-142, 1995. URL: http://dx.doi.org/10.1145/200836.200869.
http://dx.doi.org/10.1145/200836.200869
Rida A Bazzi and Yin Ding. Non-skipping timestamps for byzantine data storage systems. In International Symposium on Distributed Computing, pages 405-419. Springer, 2004.
Alon Berger, Idit Keidar, and Alexander Spiegelman. Integrated bounds for disintegrated storage. arXiv preprint arXiv:1805.06265, 2018.
Christian Cachin and Stefano Tessaro. Optimal resilience for erasure-coded byzantine distributed storage. In Dependable Systems and Networks, 2006. DSN 2006. International Conference on, pages 115-124. IEEE, 2006.
Viveck R. Cadambe, Nancy Lynch, Muriel Medard, and Peter Musial. A coded shared atomic memory algorithm for message passing architectures. In Network Computing and Applications (NCA), 2014 IEEE 13th International Symposium on, pages 253-260. IEEE, 2014.
Viveck R. Cadambe, Zhiying Wang, and Nancy Lynch. Information-theoretic lower bounds on the storage cost of shared memory emulation. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC '16, pages 305-313, New York, NY, USA, 2016. ACM. URL: http://dx.doi.org/10.1145/2933057.2933118.
http://dx.doi.org/10.1145/2933057.2933118
Soma Chaudhuri, Martha J Kosa, and Jennifer L Welch. One-write algorithms for multivalued regular and atomic registers. Acta Informatica, 37(3):161-192, 2000.
Tian Ze Chen and Yuanhao Wei. Step Optimal Implementations of Large Single-Writer Registers. In Panagiota Fatourou, Ernesto Jiménez, and Fernando Pedone, editors, 20th International Conference on Principles of Distributed Systems (OPODIS 2016), volume 70 of Leibniz International Proceedings in Informatics (LIPIcs), pages 32:1-32:16, Dagstuhl, Germany, 2017. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik. URL: http://dx.doi.org/10.4230/LIPIcs.OPODIS.2016.32.
http://dx.doi.org/10.4230/LIPIcs.OPODIS.2016.32
Gregory Chockler, Rachid Guerraoui, and Idit Keidar. Amnesic distributed storage. In Distributed Computing, pages 139-151. Springer, 2007.
Gregory Chockler and Alexander Spiegelman. Space complexity of fault-tolerant register emulations. In Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC '17, pages 83-92, New York, NY, USA, 2017. ACM. URL: http://dx.doi.org/10.1145/3087801.3087824.
http://dx.doi.org/10.1145/3087801.3087824
Dan Dobre, Ghassan Karame, Wenting Li, Matthias Majuntke, Neeraj Suri, and Marko Vukolić. Powerstore: proofs of writing for efficient and robust storage. In Proceedings of the 2013 ACM SIGSAC conference on Computer &communications security, pages 285-298. ACM, 2013.
Partha Dutta, Rachid Guerraoui, and Ron R. Levy. Optimistic erasure-coded distributed storage. In Proceedings of the 22nd International Symposium on Distributed Computing, DISC '08, pages 182-196, Berlin, Heidelberg, 2008. Springer-Verlag. URL: http://dx.doi.org/10.1007/978-3-540-87779-0_13.
http://dx.doi.org/10.1007/978-3-540-87779-0_13
Garth R Goodson, Jay J Wylie, Gregory R Ganger, and Michael K Reiter. Efficient byzantine-tolerant erasure-coded storage. In Dependable Systems and Networks, 2004 International Conference on, pages 135-144. IEEE, 2004.
Prasad Jayanti, Tushar Deepak Chandra, and Sam Toueg. Fault-tolerant wait-free shared objects. Journal of the ACM (JACM), 45(3):451-500, 1998.
Leslie Lamport. On interprocess communication. Distributed computing, 1(2):86-101, 1986.
Jean-Philippe Martin, Lorenzo Alvisi, and Michael Dahlin. Minimal byzantine storage. In International Symposium on Distributed Computing, pages 311-325. Springer, 2002.
Gary L Peterson. Concurrent reading while writing. ACM Transactions on Programming Languages and Systems (TOPLAS), 5(1):46-55, 1983.
Alexander Spiegelman, Yuval Cassuto, Gregory Chockler, and Idit Keidar. Space bounds for reliable storage: Fundamental limits of coding. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC '16, pages 249-258, New York, NY, USA, 2016. ACM. URL: http://dx.doi.org/10.1145/2933057.2933104.
http://dx.doi.org/10.1145/2933057.2933104
Zhiying Wang and Viveck R. Cadambe. On multi-version coding for distributed storage. In Communication, Control, and Computing (Allerton), 2014 52nd Annual Allerton Conference on, pages 569-575. IEEE, 2014.
Yuanhao Wei. Space complexity of implementing large shared registers. arXiv preprint arXiv:1808.00481, 2018.
Alon Berger, Idit Keidar, and Alexander Spiegelman
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Distributed Recoloring
Given two colorings of a graph, we consider the following problem: can we recolor the graph from one coloring to the other through a series of elementary changes, such that the graph is properly colored after each step?
We introduce the notion of distributed recoloring: The input graph represents a network of computers that needs to be recolored. Initially, each node is aware of its own input color and target color. The nodes can exchange messages with each other, and eventually each node has to stop and output its own recoloring schedule, indicating when and how the node changes its color. The recoloring schedules have to be globally consistent so that the graph remains properly colored at each point, and we require that adjacent nodes do not change their colors simultaneously.
We are interested in the following questions: How many communication rounds are needed (in the deterministic LOCAL model of distributed computing) to find a recoloring schedule? What is the length of the recoloring schedule? And how does the picture change if we can use extra colors to make recoloring easier?
The main contributions of this work are related to distributed recoloring with one extra color in the following graph classes: trees, 3-regular graphs, and toroidal grids.
Distributed Systems
Graph Algorithms
Local Computations
Theory of computation~Distributed computing models
Theory of computation~Graph algorithms analysis
12:1-12:17
Regular Paper
This work was supported in part by ERC Grant No. 336495 (ACDC) and ANR project DISTANCIA (ANR-17-CE40-0015).
The full version of this work is available at https://arxiv.org/abs/1802.06742.
Marthe
Bonamy
Marthe Bonamy
CNRS, LaBRI, Université de Bordeaux, France
Paul
Ouvrard
Paul Ouvrard
LaBRI, CNRS, Université de Bordeaux, France
Mikaël
Rabie
Mikaël Rabie
Aalto University, Finland
Jukka
Suomela
Jukka Suomela
Aalto University, Finland
Jara
Uitto
Jara Uitto
ETH Zürich, Switzerland
and University of Freiburg, Germany
10.4230/LIPIcs.DISC.2018.12
Pierre Aboulker, Marthe Bonamy, Nicolas Bousquet, and Louis Esperet. Distributed coloring in sparse graphs with fewer colours. arXiv preprint arXiv:1802.05582, 2018.
Leonid Barenboim. Deterministic (Δ+1)-coloring in sublinear (in Δ) time in static, dynamic and faulty networks. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (PODC), pages 345-354, 2015.
Leonid Barenboim and Michael Elkin. Distributed graph coloring: Fundamentals and recent developments. Synthesis Lectures on Distributed Computing Theory, 4(1):1-171, 2013.
Marthe Bonamy and Nicolas Bousquet. Recoloring graphs via tree decompositions. European Journal of Combinatorics, 69:200-213, 2018.
Marthe Bonamy, Nicolas Bousquet, Carl Feghali, and Matthew Johnson. On a conjecture of Mohar concerning Kempe equivalence of regular graphs. arXiv preprint arXiv:1510.06964, 2015.
Paul Bonsma and Luis Cereceda. Finding paths between graph colourings: PSPACE-completeness and superpolynomial distances. Theoretical Computer Science, 410(50):5215-5226, 2009.
Paul Bonsma, Amer E Mouawad, Naomi Nishimura, and Venkatesh Raman. The complexity of bounded length graph recoloring and CSP reconfiguration. In International Symposium on Parameterized and Exact Computation, pages 110-121. Springer, 2014.
Nicolas Bousquet and Guillem Perarnau. Fast recoloring of sparse graphs. European Journal of Combinatorics, 52:1-11, 2016.
Sebastian Brandt, Juho Hirvonen, Janne H Korhonen, Tuomo Lempiäinen, Patric RJ Östergård, Christopher Purcell, Joel Rybicki, Jukka Suomela, and Przemysław Uznański. LCL problems on grids. In Proceedings of the ACM Symposium on Principles of Distributed Computing, pages 101-110. ACM, 2017.
Luis Cereceda, Jan Van den Heuvel, and Matthew Johnson. Mixing 3-colourings in bipartite graphs. European Journal of Combinatorics, 30(7):1593-1606, 2009.
Luis Cereceda, Jan Van Den Heuvel, and Matthew Johnson. Finding paths between 3-colorings. Journal of graph theory, 67(1):69-82, 2011.
Yi-Jung Chang, Tsvi Kopelowitz, and Seth Pettie. An exponential separation between randomized and deterministic complexity in the LOCAL model. In Foundations of Computer Science (FOCS), pages 615-624, 2016.
Yi-Jung Chang, Wenzheng Li, and Seth Pettie. An optimal distributed (Δ+1)-coloring algorithm? In Proceedings of the 50th ACM Symposium on Theory of Computing (STOC), 2018.
Carl Feghali, Matthew Johnson, and Daniël Paulusma. A reconfigurations analogue of Brooks' theorem and its consequences. Journal of Graph Theory, 83(4):340-358, 2016.
Carl Feghali, Matthew Johnson, and Daniël Paulusma. Kempe equivalence of colourings of cubic graphs. European Journal of Combinatorics, 59:1-10, 2017.
Mark Jerrum. A very simple algorithm for estimating the number of k-colorings of a low-degree graph. Random Structures &Algorithms, 7(2):157-165, 1995.
Alfred B Kempe. On the geographical problem of the four colours. American Journal of Mathematics, 2(3):193-200, 1879.
Michel Las Vergnas and Henri Meyniel. Kempe classes and the Hadwiger conjecture. Journal of Combinatorial Theory, Series B, 31(1):95-104, 1981.
Daniel C McDonald. Connectedness and Hamiltonicity of graphs on vertex colorings. arXiv preprint arXiv:1507.05344, 2015.
Gary L. Miller and John H. Reif. Parallel tree contraction part 1: Fundamentals. Advances in Computing Research, 5:47-72, 1989.
Moni Naor and Larry Stockmeyer. What can be computed locally? SIAM Journal on Computing, 24(6):1259-1277, 1995.
Alessandro Panconesi and Aravind Srinivasan. Improved distributed algorithms for coloring and network decomposition problems. In Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, pages 581-592. ACM, 1992.
Alessandro Panconesi and Aravind Srinivasan. The local nature of Δ-coloring and its algorithmic applications. Combinatorica, 15(2):255-280, 1995.
Jan van den Heuvel. The complexity of change. Surveys in Combinatorics, 409(2013):127-160, 2013.
Marthe Bonamy, Paul Ouvrard, Mikaël Rabie, Jukka Suomela, and Jara Uitto
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
A Tight Lower Bound for Semi-Synchronous Collaborative Grid Exploration
Recently, there has been a growing interest in grid exploration by agents with limited capabilities. We show that the grid cannot be explored by three semi-synchronous finite automata, answering an open question by Emek et al. [TCS'15] in the negative.
In the setting we consider, time is divided into discrete steps, where in each step, an adversarially selected subset of the agents executes one look-compute-move cycle. The agents operate according to a shared finite automaton, where every agent is allowed to have a distinct initial state. The only means of communication is to sense the states of the agents sharing the same grid cell. The agents are equipped with a global compass and whenever an agent moves, the destination cell of the movement is chosen by the agent's automaton from the set of neighboring grid cells. In contrast to the four agent protocol by Emek et al., we show that three agents do not suffice for grid exploration.
Finite automata
Graph exploration
Mobile robots
Computing methodologies~Mobile agents
13:1-13:17
Regular Paper
https://arxiv.org/abs/1705.03834
Sebastian
Brandt
Sebastian Brandt
ETH Zürich, Switzerland
Jara
Uitto
Jara Uitto
ETH Zürich, Switzerland
Partially supported by ERC Grant No. 336495 (ACDC).
Roger
Wattenhofer
Roger Wattenhofer
ETH Zürich, Switzerland
10.4230/LIPIcs.DISC.2018.13
Susanne Albers and Monika Henzinger. Exploring Unknown Environments. SIAM Journal on Computing, 29:1164-1188, 2000.
Romas Aleliunas, Richard M. Karp, Richard J. Lipton, Laszlo Lovasz, and Charles Rackoff. Random Walks, Universal Traversal Sequences, and the Complexity of Maze Problems. In FOCS, pages 218-223, 1979.
Igor Averbakh and Oded Berman. A Heuristic with Worst-case Analysis for Minimax Routing of Two Travelling Salesmen on a Tree. Discrete Appl. Math., 68(1-2):17-32, 1996.
Ricardo A. Baeza-Yates, Joseph C. Culberson, and Gregory J. E. Rawlins. Searching in the Plane. Information and Computation, 106:234-252, 1993.
M. A. Bender and D. K. Slonim. The Power of Team Exploration: Two Robots can Learn Unlabeled Directed Graphs. In FOCS, pages 75-85, 1994.
M. Blum and W. J. Sakoda. On the capability of finite automata in 2 and 3 dimensional space. In FOCS, pages 147-161, 1977.
Manuel Blum and Dexter Kozen. On the Power of the Compass (or, Why Mazes Are Easier to Search Than Graphs). In FOCS, pages 132-142, 1978.
Sebastian Brandt, Jara Uitto, and Roger Wattenhofer. Tight Bounds for Asynchronous Collaborative Grid Exploration. CoRR, abs/1705.03834, 2017. URL: http://arxiv.org/abs/1705.03834.
http://arxiv.org/abs/1705.03834
Lothar Budach. Automata and Labyrinths. Mathematische Nachrichten, 86(1):195-282, 1978.
Marek Chrobak, Leszek Gasieniec, Thomas Gorry, and Russell Martin. Group Search on the Line, pages 164-176. Springer Berlin Heidelberg, 2015. URL: http://dx.doi.org/10.1007/978-3-662-46078-8_14.
http://dx.doi.org/10.1007/978-3-662-46078-8_14
Lihi Cohen, Yuval Emek, Oren Louidor, and Jara Uitto. Exploring an Infinite Space with Finite Memory Scouts. In SODA, pages 207-224, 2017.
Xiaotie Deng and Christos Papadimitriou. Exploring an Unknown Graph. Journal of Graph Theory, 32:265-297, 1999.
Krzysztof Diks, Pierre Fraigniaud, Evangelos Kranakis, and Andrzej Pelc. Tree Exploration with Little Memory. Journal of Algorithms, 51:38-63, 2004.
Yann Disser, Jan Hackfeld, and Max Klimm. Undirected Graph Exploration with Θ(log log n) Pebbles. In SODA, pages 25-39, 2016.
Christian A. Duncan, Stephen G. Kobourov, and V. S. Anil Kumar. Optimal Constrained Graph Exploration. ACM Trans. Algorithms, 2(3):380-402, 2006.
Yuval Emek, Tobias Langner, David Stolz, Jara Uitto, and Roger Wattenhofer. How Many Ants Does it Take to Find the Food? Theor. Comput. Sci., 608:255-267, 2015. URL: http://dx.doi.org/10.1016/j.tcs.2015.05.054.
http://dx.doi.org/10.1016/j.tcs.2015.05.054
Yuval Emek, Tobias Langner, Jara Uitto, and Roger Wattenhofer. Solving the ANTS Problem with Asynchronous Finite State Machines. In ICALP, pages 471-482, 2014.
Ofer Feinerman, Amos Korman, Zvi Lotker, and Jean-Sebastien Sereni. Collaborative Search on the Plane Without Communication. In PODC, pages 77-86, 2012.
P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Distributed Coordination of a Set of Autonomous Mobile Robots. In Intelligent Vehicles Symposium, pages 480-485, 2000.
Pierre Fraigniaud and David Ilcinkas. Digraphs Exploration with Little Memory, pages 246-257. Springer Berlin Heidelberg, 2004. URL: http://dx.doi.org/10.1007/978-3-540-24749-4_22.
http://dx.doi.org/10.1007/978-3-540-24749-4_22
Frank Hoffmann. One Pebble Does Not Suffice to Search Plane Labyrinths. In FCT, pages 433-444, 1981.
Alejandro López-Ortiz and Graeme Sweet. Parallel Searching on a Lattice. In CCCG, pages 125-128, 2001.
Petrişor Panaite and Andrzej Pelc. Exploring Unknown Undirected Graphs. In SODA, pages 316-322, 1998.
H. A. Rollik. Automaten in Planaren Graphen, pages 266-275. Springer Berlin Heidelberg, Berlin, Heidelberg, 1979. URL: http://dx.doi.org/10.1007/3-540-09118-1_28.
http://dx.doi.org/10.1007/3-540-09118-1_28
Kazuo Sugihara and Ichiro Suzuki. Distributed Algorithms for Formation of Geometric Patterns with Many Mobile Robots. Journal of Robotic Systems, 13(3):127-139, 1996.
Ichiro Suzuki and Masafumi Yamashita. Distributed Anonymous Mobile Robots: Formation of Geometric Patterns. SIAM Journal on Computing, 28(4):1347-1363, 1999.
Ichiro Suzuki and Masafurni Yarnashita. Distributed Anonymous Mobile Robots - Formation and Agreement Problems. In SIROCCO, pages 1347-1363, 1996.
Sebastian Brandt, Jara Uitto, and Roger Wattenhofer
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Multi-Shot Distributed Transaction Commit
Atomic Commit Problem (ACP) is a single-shot agreement problem similar to consensus, meant to model the properties of transaction commit protocols in fault-prone distributed systems. We argue that ACP is too restrictive to capture the complexities of modern transactional data stores, where commit protocols are integrated with concurrency control, and their executions for different transactions are interdependent. As an alternative, we introduce Transaction Certification Service (TCS), a new formal problem that captures safety guarantees of multi-shot transaction commit protocols with integrated concurrency control. TCS is parameterized by a certification function that can be instantiated to support common isolation levels, such as serializability and snapshot isolation. We then derive a provably correct crash-resilient protocol for implementing TCS through successive refinement. Our protocol achieves a better time complexity than mainstream approaches that layer two-phase commit on top of Paxos-style replication.
Atomic commit problem
two-phase commit
Paxos
Theory of computation~Distributed computing models
14:1-14:18
Regular Paper
Gregory
Chockler
Gregory Chockler
Royal Holloway, University of London, UK
Alexey
Gotsman
Alexey Gotsman
IMDEA Software Institute, Madrid, Spain
Alexey Gotsman was supported by an ERC Starting Grant RACCOON.
10.4230/LIPIcs.DISC.2018.14
Hal Berenson, Phil Bernstein, Jim Gray, Jim Melton, Elizabeth O'Neil, and Patrick O'Neil. A critique of ANSI SQL isolation levels. In Conference on Management of Data (SIGMOD), 1995.
Philip A Bernstein, Vassos Hadzilacos, and Nathan Goodman. Concurrency Control and Recovery in Database Systems. Addison-Wesley Longman Publishing Co., Inc., 1986.
Andrea J. Borr. Transaction monitoring in ENCOMPASS: reliable distributed transaction processing. In International Conference on Very Large Data Bases (VLDB), 1981.
Miguel Castro and Barbara Liskov. Practical byzantine fault tolerance. In Symposium on Operating Systems Design and Implementation (OSDI), 1999.
Tushar Deepak Chandra, Vassos Hadzilacos, and Sam Toueg. The weakest failure detector for solving consensus. J. ACM, 43(4), 1996.
Bernadette Charron-Bost and André Schiper. Uniform consensus is harder than consensus. J. Algorithms, 51(1), 2004.
Gregory Chockler and Alexey Gotsman. Multi-shot distributed transaction commit (extended version). arXiv CoRR, 1808.00688, 2018. Available from http://arxiv.org/abs/1808.00688.
Paulo R. Coelho, Nicolas Schiper, and Fernando Pedone. Fast atomic multicast. In Conference on Dependable Systems and Networks (DSN), 2017.
James C. Corbett, Jeffrey Dean, Michael Epstein, Andrew Fikes, Christopher Frost, J. J. Furman, Sanjay Ghemawat, Andrey Gubarev, Christopher Heiser, Peter Hochschild, Wilson C. Hsieh, Sebastian Kanthak, Eugene Kogan, Hongyi Li, Alexander Lloyd, Sergey Melnik, David Mwaura, David Nagle, Sean Quinlan, Rajesh Rao, Lindsay Rolig, Yasushi Saito, Michal Szymaniak, Christopher Taylor, Ruth Wang, and Dale Woodford. Spanner: Google’s globally-distributed database. In Symposium on Operating Systems Design and Implementation (OSDI), 2012.
Xavier Défago, André Schiper, and Péter Urbán. Total order broadcast and multicast algorithms: Taxonomy and survey. ACM Comput. Surv., 36(4), 2004.
Aleksandar Dragojević, Dushyanth Narayanan, Edmund B. Nightingale, Matthew Renzelmann, Alex Shamis, Anirudh Badam, and Miguel Castro. No compromises: Distributed transactions with consistency, availability, and performance. In Symposium on Operating Systems Principles (SOSP), 2015.
Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Consensus in the presence of partial synchrony. J. ACM, 35(2), 1988.
Cynthia Dwork and Dale Skeen. The inherent cost of nonblocking commitment. In Symposium on Principles of Distributed Computing (PODC), 1983.
Lisa Glendenning, Ivan Beschastnikh, Arvind Krishnamurthy, and Thomas Anderson. Scalable consistency in Scatter. In Symposium on Operating Systems Principles (SOSP), 2011.
Jim Gray. Notes on data base operating systems. In Operating Systems, An Advanced Course, 1978.
Jim Gray and Leslie Lamport. Consensus on transaction commit. ACM Trans. Database Syst., 31(1), 2006.
Rachid Guerraoui. Revisiting the relationship between non-blocking atomic commitment and consensus. In Workshop on Distributed Algorithms (WDAG), 1995.
Rachid Guerraoui, Mikel Larrea, and André Schiper. Reducing the cost for non-blocking in atomic commitment. In International Conference on Distributed Computing Systems (ICDCS), 1996.
Rachid Guerraoui and Jingjing Wang. How fast can a distributed transaction commit? In Symposium on Principles of Database Systems (PODS), 2017.
V. Hadzilacos. On the relationship between the atomic commitment and consensus problems. In Asilomar Workshop on Fault-Tolerant Distributed Computing, 1990.
Maurice P. Herlihy and Jeannette M. Wing. Linearizability: A correctness condition for concurrent objects. ACM Trans. Program. Lang. Syst., 12(3), 1990.
Flavio Paiva Junqueira, Benjamin C. Reed, and Marco Serafini. Zab: High-performance broadcast for primary-backup systems. In Conference on Dependable Systems and Networks (DSN), 2011.
Idit Keidar and Danny Dolev. Increasing the resilience of atomic commit at no additional cost. In Symposium on Principles of Database Systems (PODS), 1995.
Idit Keidar and Sergio Rajsbaum. A simple proof of the uniform consensus synchronous lower bound. Inf. Process. Lett., 85(1), 2003.
Maciej Kokocinski, Tadeusz Kobus, and Pawel T. Wojciechowski. Make the leader work: Executive deferred update replication. In Symposium on Reliable Distributed Systems (SRDS), 2014.
Tim Kraska, Gene Pang, Michael J. Franklin, Samuel Madden, and Alan Fekete. MDCC: Multi-data center consistency. In European Conference on Computer Systems (EuroSys), 2013.
Leslie Lamport. The part-time parliament. ACM Trans. Comput. Syst., 16(2), 1998.
Hatem Mahmoud, Faisal Nawab, Alexander Pucher, Divyakant Agrawal, and Amr El Abbadi. Low-latency multi-datacenter databases using replicated commit. Proc. VLDB Endow., 6(9), 2013.
Brian M. Oki and Barbara H. Liskov. Viewstamped replication: A new primary copy method to support highly-available distributed systems. In Symposium on Principles of Distributed Computing (PODC), 1988.
Fernando Pedone, Rachid Guerraoui, and André Schiper. The database state machine approach. Distributed and Parallel Databases, 14(1), 2003.
Sebastiano Peluso, Paolo Romano, and Francesco Quaglia. Score: A scalable one-copy serializable partial replication protocol. In International Middleware Conference (Middleware), 2012.
Sebastiano Peluso, Pedro Ruivo, Paolo Romano, Francesco Quaglia, and Luís E. T. Rodrigues. GMU: genuine multiversion update-serializable partial data replication. IEEE Trans. Parallel Distrib. Syst., 27(10), 2016.
K. V. S. Ramarao. Complexity of distributed commit protocols. Acta Informatica, 26(6), 1989.
Masoud Saeida Ardekani, Pierre Sutra, and Marc Shapiro. G-DUR: A middleware for assembling, analyzing, and improving transactional protocols. In International Middleware Conference (Middleware), 2014.
Nicolas Schiper, Pierre Sutra, and Fernando Pedone. P-store: Genuine partial replication in wide area networks. In Symposium on Reliable Distributed Systems (SRDS), 2010.
Fred B. Schneider. Implementing fault-tolerant services using the state machine approach: A tutorial. ACM Comput. Surv., 22(4), 1990.
Daniele Sciascia, Fernando Pedone, and Flavio Junqueira. Scalable deferred update replication. In Conference on Dependable Systems and Networks (DSN), 2012.
Dale Skeen. Nonblocking commit protocols. In Conference on Management of Data (SIGMOD), 1981.
Yair Sovran, Russell Power, Marcos K. Aguilera, and Jinyang Li. Transactional storage for geo-replicated systems. In Symposium on Operating Systems Principles (SOSP), 2011.
Gerhard Weikum and Gottfried Vossen. Transactional Information Systems: Theory, Algorithms, and the Practice of Concurrency Control and Recovery. Morgan Kaufmann Publishers Inc., 2001.
Irene Zhang, Naveen Kr. Sharma, Adriana Szekeres, Arvind Krishnamurthy, and Dan R. K. Ports. Building consistent transactions with inconsistent replication. In Symposium on Operating Systems Principles (SOSP), 2015.
Irene Zhang, Naveen Kr. Sharma, Adriana Szekeres, Arvind Krishnamurthy, and Dan R. K. Ports. When is operation ordering required in replicated transactional storage? IEEE Data Eng. Bull., 39(1), 2016.
Gregory Chockler and Alexey Gotsman
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Deterministic Blind Radio Networks
Ad-hoc radio networks and multiple access channels are classical and well-studied models of distributed systems, with a large body of literature on deterministic algorithms for fundamental communications primitives such as broadcasting and wake-up. However, almost all of these algorithms assume knowledge of the number of participating nodes and the range of possible IDs, and often make the further assumption that the latter is linear in the former. These are very strong assumptions for models which were designed to capture networks of weak devices organized in an ad-hoc manner. It was believed that without this knowledge, deterministic algorithms must necessarily be much less efficient.
In this paper we address this fundamental question and show that this is not the case. We present deterministic algorithms for blind networks (in which nodes know only their own IDs), which match or nearly match the running times of the fastest algorithms which assume network knowledge (and even surpass the previous fastest algorithms which assume parameter knowledge but not small labels).
Specifically, in multiple access channels with k participating nodes and IDs up to L, we give a wake-up algorithm requiring O((k log L log k)/(log log k)) time, improving dramatically over the O(L^3 log^3 L) time algorithm of De Marco et al. (2007), and a broadcasting algorithm requiring O(k log L log log k) time, improving over the O(L) time algorithm of Gasieniec et al. (2001) in most circumstances. Furthermore, we show how these same algorithms apply directly to multi-hop radio networks, achieving even larger running time improvements.
Broadcasting
Deterministic Algorithms
Radio Networks
Theory of computation~Distributed algorithms
Networks~Network algorithms
15:1-15:17
Regular Paper
Research partially supported by the Centre for Discrete Mathematics and its Applications (DIMAP), by EPSRC award EP/D063191/1, and by EPSRC award EP/N011163/1.
Artur
Czumaj
Artur Czumaj
University of Warwick, Coventry, UK
Peter
Davies
Peter Davies
University of Warwick, Coventry, UK
10.4230/LIPIcs.DISC.2018.15
N. Alon, A. Bar-Noy, N. Linial, and D. Peleg. A lower bound for radio broadcast. Journal of Computer and System Sciences, 43(2):290-298, 1991.
R. Bar-Yehuda, O. Goldreich, and A. Itai. On the time-complexity of broadcast in multi-hop radio networks: An exponential gap between determinism and randomization. Journal of Computer and System Sciences, 45(1):104-126, 1992.
B. Chlebus, L. Gasieniec, D. R. Kowalski, and T. Radzik. On the wake-up problem in radio networks. In Proceedings of the 32nd Annual International Colloquium on Automata, Languages and Programming (ICALP), pages 347-359, 2005.
B. Chlebus and D. R. Kowalski. A better wake-up in radio networks. In Proceedings of the 23rd Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 266-274, 2004.
B. Chlebus and D. R. Kowalski. Almost optimal explicit selectors. In Proceedings of the 15th International Symposium on Fundamentals of Computation Theory (FCT), pages 270-280, 2005.
B. S. Chlebus, L. Gasieniec, A. Gibbons, A. Pelc, and W. Rytter. Deterministic broadcasting in unknown radio networks. Distributed Computing, 15(1):27-38, 2002.
B. S. Chlebus, L. Gasieniec, A. Östlin, and J. M. Robson. Deterministic radio broadcasting. In Proceedings of the 27th Annual International Colloquium on Automata, Languages and Programming (ICALP), pages 717-728, 2000.
M. Chrobak, L. Gasieniec, and D. R. Kowalski. The wake-up problem in multihop radio networks. SIAM Journal on Computing, 36(5):1453-1471, 2007.
M. Chrobak, L. Gasieniec, and W. Rytter. Fast broadcasting and gossiping in radio networks. Journal of Algorithms, 43(2):177-189, 2002.
A. E. F. Clementi, A. Monti, and R. Silvestri. Distributed broadcasting in radio networks of unknown topology. Theoretical Computer Science, 302(1-3):337-364, 2003.
A. Czumaj and P. Davies. Exploiting spontaneous transmissions for broadcasting and leader election in radio networks. In Proceedings of the 36th Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 3-12, 2017.
A. Czumaj and P. Davies. Brief announcement: Randomized blind radio networks. In Proceedings of the 32nd International Symposium on Distributed Computing (DISC), pages 44:1-44:3, 2018.
A. Czumaj and P. Davies. Deterministic communication in radio networks. SIAM Journal on Computing, 47(1):218-240, 2018.
A. Czumaj and W. Rytter. Broadcasting algorithms in radio networks with unknown topology. In Proceedings of the 44th IEEE Symposium on Foundations of Computer Science (FOCS), pages 492-501, 2003.
L. Gasieniec, A. Pelc, and D. Peleg. The wakeup problem in synchronous broadcast systems. SIAM Journal on Discrete Mathematics, 14(2):207-222, 2001.
M. Ghaffari, B. Haeupler, and M. Khabbazian. Randomized broadcast in radio networks with collision detection. In Proceedings of the 32nd Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 325-334, 2013.
B. Haeupler and D. Wajc. A faster distributed radio broadcast primitive. In Proceedings of the 35th Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 361-370, 2016.
P. Indyk. Explicit constructions of selectors and related combinatorial structures, with applications. In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 697-704, 2002.
T. Jurdziński and G. Stachowiak. Probabilistic algorithms for the wakeup problem in single-hop radio networks. Theory of Computing Systems, 38(3):347-367, 2005.
D. Kowalski. On selection problem in radio networks. In Proceedings of the 24th Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 158-166, 2005.
D. Kowalski and A. Pelc. Faster deterministic broadcasting in ad hoc radio networks. SIAM Journal on Discrete Mathematics, 18(2):332-346, 2004.
D. Kowalski and A. Pelc. Broadcasting in undirected ad hoc radio networks. Distributed Computing, 18(1):43-57, 2005.
E. Kushilevitz and Y. Mansour. An Ω(D log(N/D)) lower bound for broadcast in radio networks. SIAM Journal on Computing, 27(3):702-712, 1998.
G. De Marco. Distributed broadcast in unknown radio networks. SIAM Journal on Computing, 39(6):2162-2175, 2010.
G. De Marco and A. Pelc. Faster broadcasting in unknown radio networks. Information Processing Letters, 79(2):53-56, 2001.
G. De Marco, M. Pelegrini, and G. Sburlati. Faster deterministic wakeup in multiple access channels. Discrete Apllied Mathematics, 155(8):898-903, 2007.
D. Peleg. Time-efficient broadcasting in radio networks: A review. In Proceedings of the 4th International Conference on Distributed Computing and Internet Technology (ICDCIT), pages 1-18, 2007.
D. E. Willard. Log-logarithmic selection resolution protocols in a multiple access channel. SIAM Journal on Computing, 15(2):468-477, 1986.
Artur Czumaj and Peter Davies
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Detecting Cliques in CONGEST Networks
The problem of detecting network structures plays a central role in distributed computing. One of the fundamental problems studied in this area is to determine whether for a given graph H, the input network contains a subgraph isomorphic to H or not. We investigate this problem for H being a clique K_l in the classical distributed CONGEST model, where the communication topology is the same as the topology of the underlying network, and with limited communication bandwidth on the links.
Our first and main result is a lower bound, showing that detecting K_l requires Omega(sqrt{n} / b) communication rounds, for every 4 <=l <=sqrt{n}, and Omega(n / (l b)) rounds for every l >= sqrt{n}, where b is the bandwidth of the communication links. This result is obtained by using a reduction to the set disjointness problem in the framework of two-party communication complexity. We complement our lower bound with a two-party communication protocol for listing all cliques in the input graph, which up to constant factors communicates the same number of bits as our lower bound for K_4 detection. This demonstrates that our lower bound cannot be improved using the two-party communication framework.
Lower bounds
CONGEST
subgraph detection
two-party communication
Theory of computation~Distributed algorithms
Networks~Network algorithms
16:1-16:15
Regular Paper
Artur
Czumaj
Artur Czumaj
Department of Computer Science and Centre for Discrete Mathematics and its Applications (DIMAP), University of Warwick, UK
Research partially supported by the Centre for Discrete Mathematics and its Applications (DIMAP), by EPSRC award EP/D063191/1, by EPSRC award EP/N011163/1, and by an IBM Faculty Award.
Christian
Konrad
Christian Konrad
Department of Computer Science, University of Bristol, UK
Most of work on this paper has been carried out while the author was at the University of Warwick, where he was supported by the Centre for Discrete Mathematics and its Applications (DIMAP) and by EPSRC award EP/N011163/1.
10.4230/LIPIcs.DISC.2018.16
Zvika Brakerski and Boaz Patt-Shamir. Distributed discovery of large near-cliques. Distributed Computing, 24(2):79-89, 2011.
Keren Censor-Hillel, Eldar Fischer, Gregory Schwartzman, and Yadu Vasudev. Fast distributed algorithms for testing graph properties. In Proceedings of the 30th International Symposium on Distributed Computing (DISC), pages 43-56, 2016.
Keren Censor-Hillel, Petteri Kaski, Janne H. Korhonen, Christoph Lenzen, Ami Paz, and Jukka Suomela. Algebraic methods in the congested clique. In Proceedings of the 35th Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 143-152, 2015.
Keren Censor-Hillel, Seri Khoury, and Ami Paz. Quadratic and near-quadratic lower bounds for the CONGEST model. In Proceedings of the 31st International Symposium on Distributed Computing (DISC), pages 10:1-10:16, 2017.
Yi-Jun Chang, Seth Pettie, and Hengjie Zhang. Distributed triangle detection via expander decomposition. CoRR, abs/1807.06624, 2018. URL: http://arxiv.org/abs/1807.06624.
http://arxiv.org/abs/1807.06624
Danny Dolev, Christoph Lenzen, and Shir Peled. "Tri, tri again": Finding triangles and small subgraphs in a distributed setting. In Proceedings of the 26th International Symposium on Distributed Computing (DISC), pages 195-209, 2012.
Andrew Drucker, Fabian Kuhn, and Rotem Oshman. On the power of the congested clique model. In Proceedings of the 33rd Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 367-376, 2014.
Guy Even, Orr Fischer, Pierre Fraigniaud, Tzlil Gonen, Reut Levi, Moti Medina, Pedro Montealegre, Dennis Olivetti, Rotem Oshman, Ivan Rapaport, and Ioan Todinca. Three notes on distributed property testing. In Proceedings of the 31st International Symposium on Distributed Computing (DISC), pages 15:1-15:30, 2017.
Orr Fischer, Tzlil Gonen, Fabian Kuhn, and Rotem Oshman. Possibilities and impossibilities for distributed subgraph detection. In Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures, (SPAA), pages 153-162, New York, NY, USA, 2018. ACM.
Pierre Fraigniaud and Dennis Olivetti. Distributed detection of cycles. In Proceedings of the 29th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 153-162, 2017.
Tzlil Gonen and Rotem Oshman. Lower bounds for subgraph detection in the CONGEST model. In Proceedings of the 21st International Conference on Principles of Distributed Systems (OPODIS), pages 6:1-6:16, 2017.
Taisuke Izumi and François Le Gall. Triangle finding and listing in CONGEST networks. In Proceedings of the 37th Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 381-389, 2017.
Svante Janson, Tomasz Łuczak, and Andrzej Ruciński. Random Graphs. John Wiley &Sons, 2011.
Bala Kalyanasundaram and Georg Schnitger. The probabilistic communication complexity of set intersection. SIAM Journal on Discrete Mathematics, 5(4):545-557, 1992.
Janne H. Korhonen and Joel Rybicki. Deterministic subgraph detection in broadcast CONGEST. In Proceedings of the 21st International Conference on Principles of Distributed Systems (OPODIS), pages 4:1-4:16, 2017.
Eyal Kushilevitz and Noam Nisan. Communication Complexity. Cambridge University Press, 1997.
Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. Tight bounds for distributed graph computations. CoRR, abs/1602.08481, 2016.
David Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia, PA, 2000.
Artur Czumaj and Christian Konrad
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
A Wealth of Sub-Consensus Deterministic Objects
The consensus hierarchy classifies shared an object according to its consensus number, which is the maximum number of processes that can solve consensus wait-free using the object. The question of whether this hierarchy is precise enough to fully characterize the synchronization power of deterministic shared objects was open until 2016, when Afek et al. showed that there is an infinite hierarchy of deterministic objects, each weaker than the next, which is strictly between i and i+1-processors consensus, for i >= 2. For i=1, the question whether there exist a deterministic object whose power is strictly between read-write and 2-processors consensus, remained open.
We resolve the question positively by exhibiting an infinite hierarchy of simple deterministic objects which are equivalent to set-consensus tasks, and thus are stronger than read-write registers, but they cannot implement consensus for two processes. Still our paper leaves a gap with open questions.
shared memory
distributed algorithms
wait-free
set consensus
Theory of computation~Distributed computing models
17:1-17:17
Regular Paper
The work of Yehuda Afek and Eli Gafni was partially supported by the United States-Israel Binational Science Foundation (grant 2014226). This material is based upon work supported by the National Science Foundation under Grant No. 1655166.
Eli
Daian
Eli Daian
School of Computer Science, Tel-Aviv University, Israel
Giuliano
Losa
Giuliano Losa
Computer Science Department, University of California, Los Angeles, CA, USA
Yehuda
Afek
Yehuda Afek
School of Computer Science, Tel-Aviv University, Israel
Eli
Gafni
Eli Gafni
Computer Science Department, University of California, Los Angeles, CA, USA
10.4230/LIPIcs.DISC.2018.17
Yehuda Afek, Faith Ellen, and Eli Gafni. Deterministic objects: Life beyond consensus. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC '16, pages 97-106, New York, NY, USA, 2016. ACM. URL: http://dx.doi.org/10.1145/2933057.2933116.
http://dx.doi.org/10.1145/2933057.2933116
Yehuda Afek, Eli Gafni, and Adam Morrison. Common2 extended to stacks and unbounded concurrency. Distributed Computing, 20(4):239-252, Nov 2007. URL: http://dx.doi.org/10.1007/s00446-007-0023-3.
http://dx.doi.org/10.1007/s00446-007-0023-3
Yehuda Afek, Eli Gafni, Sergio Rajsbaum, Michel Raynal, and Corentin Travers. Simultaneous consensus tasks: A tighter characterization of set-consensus. In Soma Chaudhuri, Samir R. Das, Himadri S. Paul, and Srikanta Tirthapura, editors, Distributed Computing and Networking, pages 331-341, Berlin, Heidelberg, 2006. Springer Berlin Heidelberg.
Yehuda Afek and Michael Merritt. Fast, wait-free (2k-1)-renaming. In Proceedings of the Eighteenth Annual ACM Symposium on Principles of Distributed Computing, PODC '99, pages 105-112, New York, NY, USA, 1999. ACM. URL: http://dx.doi.org/10.1145/301308.301338.
http://dx.doi.org/10.1145/301308.301338
Yehuda Afek, Eytan Weisberger, and Hanan Weisman. A completeness theorem for a class of synchronization objects. In Proceedings of the Twelfth Annual ACM Symposium on Principles of Distributed Computing, PODC '93, pages 159-170, New York, NY, USA, 1993. ACM. URL: http://dx.doi.org/10.1145/164051.164071.
http://dx.doi.org/10.1145/164051.164071
Hagit Attiya and Arie Fouren. Adaptive wait-free algorithms for lattice agreement and renaming (extended abstract). In Proceedings of the Seventeenth Annual ACM Symposium on Principles of Distributed Computing, PODC '98, pages 277-286, New York, NY, USA, 1998. ACM. URL: http://dx.doi.org/10.1145/277697.277749.
http://dx.doi.org/10.1145/277697.277749
Rida A. Bazzi, Gil Neiger, and Gary L. Peterson. On the use of registers in achieving wait-free consensus. Distributed Computing, 10(3):117-127, Mar 1997. URL: http://dx.doi.org/10.1007/s004460050029.
http://dx.doi.org/10.1007/s004460050029
Elizabeth Borowsky. Capturing the Power of Resiliency and Set Consensus in Distributed Systems. PhD thesis, University of California in Los Angeles, Los Angeles, CA, USA, 1995. UMI Order No. GAX96-10429.
Elizabeth Borowsky and Eli Gafni. Generalized flp impossibility result for t-resilient asynchronous computations. In Proceedings of the Twenty-fifth Annual ACM Symposium on Theory of Computing, STOC '93, pages 91-100, New York, NY, USA, 1993. ACM. URL: http://dx.doi.org/10.1145/167088.167119.
http://dx.doi.org/10.1145/167088.167119
Elizabeth Borowsky and Eli Gafni. The implication of the Borowsky-Gafni simulation on the set-consensus hierarchy. UCLA Computer Science Department, 1993.
Elizabeth Borowsky, Eli Gafni, and Yehuda Afek. Consensus power makes (some) sense! (extended abstract). In Proceedings of the Thirteenth Annual ACM Symposium on Principles of Distributed Computing, PODC '94, pages 363-372, New York, NY, USA, 1994. ACM. URL: http://dx.doi.org/10.1145/197917.198126.
http://dx.doi.org/10.1145/197917.198126
David Yu Cheng Chan, Vassos Hadzilacos, and Sam Toueg. On the number of objects with distinct power and the linearizability of set agreement objects. In 31st International Symposium on Distributed Computing, DISC 2017, October 16-20, 2017, Vienna, Austria, pages 12:1-12:14, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.DISC.2017.12.
http://dx.doi.org/10.4230/LIPIcs.DISC.2017.12
David Yu Cheng Chan, Vassos Hadzilacos, and Sam Toueg. On the classification of deterministic objects via set agreement power. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC '18, pages 71-80, New York, NY, USA, 2018. ACM. URL: http://dx.doi.org/10.1145/3212734.3212775.
http://dx.doi.org/10.1145/3212734.3212775
Soma Chaudhuri. Agreement is harder than consensus: Set consensus problems in totally asynchronous systems. In Proceedings of the Ninth Annual ACM Symposium on Principles of Distributed Computing, PODC '90, pages 311-324, New York, NY, USA, 1990. ACM. URL: http://dx.doi.org/10.1145/93385.93431.
http://dx.doi.org/10.1145/93385.93431
Soma Chaudhuri. More choices allow more faults: Set consensus problems in totally asynchronous systems. Information and Computation, 105(1):132-158, 1993.
Soma Chaudhuri and Paul Reiners. Understanding the set consensus partial order using the borowsky-gafni simulation. In Özalp Babaoğlu and Keith Marzullo, editors, Distributed Algorithms, pages 362-379, Berlin, Heidelberg, 1996. Springer Berlin Heidelberg.
Michael J. Fischer, Nancy A. Lynch, and Mike Paterson. Impossibility of distributed consensus with one faulty process. J. ACM, 32(2):374-382, 1985.
Maurice Herlihy. Impossibility results for asynchronous pram (extended abstract). In Proceedings of the Third Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA '91, pages 327-336, New York, NY, USA, 1991. ACM. URL: http://dx.doi.org/10.1145/113379.113409.
http://dx.doi.org/10.1145/113379.113409
Maurice Herlihy. Wait-free synchronization. ACM Transactions on Programming Languages and Systems (TOPLAS), 13:124-149, January 1991. URL: http://dx.doi.org/10.1145/114005.102808.
http://dx.doi.org/10.1145/114005.102808
Prasad Jayanti. Wait-free computing. In Jean-Michel Hélary and Michel Raynal, editors, Distributed Algorithms, pages 19-50, Berlin, Heidelberg, 1995. Springer Berlin Heidelberg.
Leslie Lamport. Solved problems, unsolved problems and non-problems in concurrency. SIGOPS Oper. Syst. Rev., 19(4):34-44, 1985. URL: http://dx.doi.org/10.1145/858336.858339.
http://dx.doi.org/10.1145/858336.858339
Eli Daian, Giuliano Losa, Yehuda Afek, and Eli Gafni
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
NUMASK: High Performance Scalable Skip List for NUMA
This paper presents NUMASK, a skip list data structure specifically designed to exploit the characteristics of Non-Uniform Memory Access (NUMA) architectures to improve performance. NUMASK deploys an architecture around a concurrent skip list so that all metadata accesses (e.g., traversals of the skip list index levels) read and write memory blocks allocated in the NUMA zone where the thread is executing. To the best of our knowledge, NUMASK is the first NUMA-aware skip list design that goes beyond merely limiting the performance penalties introduced by NUMA, and leverages the NUMA architecture to outperform state-of-the-art concurrent high-performance implementations. We tested NUMASK on a four-socket server. Its performance scales for both read-intensive and write-intensive workloads (tested up to 160 threads). In write-intensive workload, NUMASK shows speedups over competitors in the range of 2x to 16x.
Skip list
NUMA
Concurrent Data Structure
Information systems~Data structures
18:1-18:19
Regular Paper
This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-17-1-0367 and by the National Science Foundation under Grant No. CNS-1814974.
Henry
Daly
Henry Daly
Lehigh University, Bethlehem, PA, USA
Ahmed
Hassan
Ahmed Hassan
Alexandria University, Alexandria, Egypt
Michael F.
Spear
Michael F. Spear
Lehigh University, Bethlehem, PA, USA
Roberto
Palmieri
Roberto Palmieri
Lehigh University, Bethlehem, PA, USA
10.4230/LIPIcs.DISC.2018.18
numa(3) Linux Programmer’s Manual, second edition, December 2007. URL: https://linux.die.net/man/3/numa.
https://linux.die.net/man/3/numa
Emery D. Berger, Kathryn S. McKinley, Robert D. Blumofe, and Paul R. Wilson. Hoard: A scalable memory allocator for multithreaded applications. In Larry Rudolph and Anoop Gupta, editors, ASPLOS-IX Proceedings of the 9th International Conference on Architectural Support for Programming Languages and Operating Systems, Cambridge, MA, USA, November 12-15, 2000., pages 117-128. ACM Press, 2000. Source code available at https://github.com/emeryberger/Hoard. URL: http://dx.doi.org/10.1145/356989.357000.
http://dx.doi.org/10.1145/356989.357000
Sergey Blagodurov, Sergey Zhuravlev, Alexandra Fedorova, and Ali Kamali. A case for numa-aware contention management on multicore systems. In Proceedings of the 19th International Conference on Parallel Architectures and Compilation Techniques, PACT '10, pages 557-558, New York, NY, USA, 2010. ACM. URL: http://dx.doi.org/10.1145/1854273.1854350.
http://dx.doi.org/10.1145/1854273.1854350
Trevor Brown, Alex Kogan, Yossi Lev, and Victor Luchangco. Investigating the performance of hardware transactions on a multi-socket machine. In Christian Scheideler and Seth Gilbert, editors, Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2016, Asilomar State Beach/Pacific Grove, CA, USA, July 11-13, 2016, pages 121-132. ACM, 2016. URL: http://dx.doi.org/10.1145/2935764.2935796.
http://dx.doi.org/10.1145/2935764.2935796
Irina Calciu, Dave Dice, Yossi Lev, Victor Luchangco, Virendra J. Marathe, and Nir Shavit. NUMA-aware Reader-writer Locks. In PPoPP '13, 2013.
Irina Calciu, Siddhartha Sen, Mahesh Balakrishnan, and Marcos K. Aguilera. Black-box concurrent data structures for NUMA architectures. In Yunji Chen, Olivier Temam, and John Carter, editors, Proceedings of the Twenty-Second International Conference on Architectural Support for Programming Languages and Operating Systems, ASPLOS 2017, Xi'an, China, April 8-12, 2017, pages 207-221. ACM, 2017. URL: http://dx.doi.org/10.1145/3037697.3037721.
http://dx.doi.org/10.1145/3037697.3037721
Tyler Crain, Vincent Gramoli, and Michel Raynal. A speculation-friendly binary search tree. In J. Ramanujam and P. Sadayappan, editors, Proceedings of the 17th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPOPP 2012, New Orleans, LA, USA, February 25-29, 2012, pages 161-170. ACM, 2012. URL: http://dx.doi.org/10.1145/2145816.2145837.
http://dx.doi.org/10.1145/2145816.2145837
Tyler Crain, Vincent Gramoli, and Michel Raynal. No hot spot non-blocking skip list. In IEEE 33rd International Conference on Distributed Computing Systems, ICDCS 2013, 8-11 July, 2013, Philadelphia, Pennsylvania, USA, pages 196-205. IEEE Computer Society, 2013. URL: http://dx.doi.org/10.1109/ICDCS.2013.42.
http://dx.doi.org/10.1109/ICDCS.2013.42
Mohammad Dashti, Alexandra Fedorova, Justin R. Funston, Fabien Gaud, Renaud Lachaize, Baptiste Lepers, Vivien Quéma, and Mark Roth. Traffic management: a holistic approach to memory placement on NUMA systems. In Vivek Sarkar and Rastislav Bodík, editors, Architectural Support for Programming Languages and Operating Systems, ASPLOS '13, Houston, TX, USA - March 16 - 20, 2013, pages 381-394. ACM, 2013. URL: http://dx.doi.org/10.1145/2451116.2451157.
http://dx.doi.org/10.1145/2451116.2451157
Tudor David, Rachid Guerraoui, and Vasileios Trigonakis. Asynchronized concurrency: The secret to scaling concurrent search data structures. In Özcan Özturk, Kemal Ebcioglu, and Sandhya Dwarkadas, editors, Proceedings of the Twentieth International Conference on Architectural Support for Programming Languages and Operating Systems, ASPLOS '15, Istanbul, Turkey, March 14-18, 2015, pages 631-644. ACM, 2015. URL: http://dx.doi.org/10.1145/2694344.2694359.
http://dx.doi.org/10.1145/2694344.2694359
David Dice, Virendra J. Marathe, and Nir Shavit. Lock Cohorting: A General Technique for Designing NUMA Locks. In PPoPP '12, 2012.
Ian Dick, Alan Fekete, and Vincent Gramoli. A skip list for multicore. Concurrency and Computation: Practice and Experience, 29(4), 2017. URL: http://dx.doi.org/10.1002/cpe.3876.
http://dx.doi.org/10.1002/cpe.3876
Jason Evans. jemalloc memory allocator. URL: https://github.com/jemalloc/jemalloc.
https://github.com/jemalloc/jemalloc
Mikhail Fomitchev and Eric Ruppert. Lock-free linked lists and skip lists. In Proceedings of the Twenty-third Annual ACM Symposium on Principles of Distributed Computing, PODC '04, pages 50-59, New York, NY, USA, 2004. ACM. URL: http://dx.doi.org/10.1145/1011767.1011776.
http://dx.doi.org/10.1145/1011767.1011776
Keir Fraser. Practical lock-freedom. PhD thesis, University of Cambridge, September 2003.
Fabien Gaud, Baptiste Lepers, Justin Funston, Mohammad Dashti, Alexandra Fedorova, Vivien Quéma, Renaud Lachaize, and Mark Roth. Challenges of memory management on modern numa systems. Commun. ACM, 58(12):59-66, 2015. URL: http://dx.doi.org/10.1145/2814328.
http://dx.doi.org/10.1145/2814328
Vincent Gramoli. More than you ever wanted to know about synchronization: synchrobench, measuring the impact of the synchronization on concurrent algorithms. In Albert Cohen and David Grove, editors, Proceedings of the 20th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPoPP 2015, San Francisco, CA, USA, February 7-11, 2015, pages 1-10. ACM, 2015. URL: http://dx.doi.org/10.1145/2688500.2688501.
http://dx.doi.org/10.1145/2688500.2688501
Ahmed Hassan, Roberto Palmieri, and Binoy Ravindran. Transactional interference-less balanced tree. In Distributed Computing - 29th International Symposium, DISC 2015, Tokyo, Japan, October 7-9, 2015, Proceedings, pages 325-340, 2015.
Danny Hendler, Itai Incze, Nir Shavit, and Moran Tzafrir. Flat combining and the synchronization-parallelism tradeoff. In Proceedings of the Twenty-second Annual ACM Symposium on Parallelism in Algorithms and Architectures, SPAA '10, pages 355-364, New York, NY, USA, 2010. ACM. URL: http://dx.doi.org/10.1145/1810479.1810540.
http://dx.doi.org/10.1145/1810479.1810540
M. Herlihy and N. Shavit. The art of multiprocessor programming. Morgan Kaufmann, 2008.
Maurice Herlihy, Yossi Lev, Victor Luchangco, and Nir Shavit. A simple optimistic skiplist algorithm. In Structural Information and Communication Complexity, 14th International Colloquium, SIROCCO 2007, Castiglioncello, Italy, June 5-8, 2007, Proceedings, pages 124-138, 2007.
Christoph Lameter. Numa (non-uniform memory access): An overview. Queue, 11(7):40:40-40:51, 2013. URL: http://dx.doi.org/10.1145/2508834.2513149.
http://dx.doi.org/10.1145/2508834.2513149
Baptiste Lepers, Vivien Quéma, and Alexandra Fedorova. Thread and memory placement on NUMA systems: Asymmetry matters. In Shan Lu and Erik Riedel, editors, 2015 USENIX Annual Technical Conference, USENIX ATC '15, July 8-10, Santa Clara, CA, USA, pages 277-289. USENIX Association, 2015. URL: https://www.usenix.org/conference/atc15/technical-session/presentation/lepers.
https://www.usenix.org/conference/atc15/technical-session/presentation/lepers
Zoltan Majo and Thomas R. Gross. Memory management in numa multicore systems: Trapped between cache contention and interconnect overhead. In Proceedings of the International Symposium on Memory Management, ISMM '11, pages 11-20, New York, NY, USA, 2011. ACM. URL: http://dx.doi.org/10.1145/1993478.1993481.
http://dx.doi.org/10.1145/1993478.1993481
Mohamed Mohamedin, Roberto Palmieri, Sebastiano Peluso, and Binoy Ravindran. On designing numa-aware concurrency control for scalable transactional memory. In Rafael Asenjo and Tim Harris, editors, Proceedings of the 21st ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPoPP 2016, Barcelona, Spain, March 12-16, 2016, pages 45:1-45:2. ACM, 2016. URL: http://dx.doi.org/10.1145/2851141.2851189.
http://dx.doi.org/10.1145/2851141.2851189
Stanko Novakovic, Alexandros Daglis, Edouard Bugnion, Babak Falsafi, and Boris Grot. Scale-out NUMA. In Rajeev Balasubramonian, Al Davis, and Sarita V. Adve, editors, Architectural Support for Programming Languages and Operating Systems, ASPLOS '14, Salt Lake City, UT, USA, March 1-5, 2014, pages 3-18. ACM, 2014. URL: http://dx.doi.org/10.1145/2541940.2541965.
http://dx.doi.org/10.1145/2541940.2541965
Iraklis Psaroudakis, Stefan Kaestle, Matthias Grimmer, Daniel Goodman, Jean-Pierre Lozi, and Timothy L. Harris. Analytics with smart arrays: adaptive and efficient language-independent data. In Rui Oliveira, Pascal Felber, and Y. Charlie Hu, editors, Proceedings of the Thirteenth EuroSys Conference, EuroSys 2018, Porto, Portugal, April 23-26, 2018, pages 17:1-17:15. ACM, 2018. URL: http://dx.doi.org/10.1145/3190508.3190514.
http://dx.doi.org/10.1145/3190508.3190514
William Pugh. Skip lists: A probabilistic alternative to balanced trees. Commun. ACM, 33(6):668-676, 1990. URL: http://dx.doi.org/10.1145/78973.78977.
http://dx.doi.org/10.1145/78973.78977
Nikita Shamgunov. The memsql in-memory database system. In Justin J. Levandoski and Andrew Pavlo, editors, Proceedings of the 2nd International Workshop on In Memory Data Management and Analytics, IMDM 2014, Hangzhou, China, September 1, 2014., 2014.
Dmitry Vyukov. Unbounded SPSC Queue, 2018. URL: http://www.1024cores.net/home/lock-free-algorithms/queues/unbounded-spsc-queue.
http://www.1024cores.net/home/lock-free-algorithms/queues/unbounded-spsc-queue
Henry Daly and Ahmed Hassan and Michael F. Spear and Roberto Palmieri
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
TuringMobile: A Turing Machine of Oblivious Mobile Robots with Limited Visibility and Its Applications
In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward its destination. Each robot is punctiform and memoryless, it operates in R^m, it has a local reference system independent of the other robots' ones, and is activated asynchronously by an adversarial scheduler. Moreover, the robots are non-rigid, in that they may be stopped by the scheduler at each move before reaching their destination (but are guaranteed to travel at least a fixed unknown distance before being stopped).
We show that despite these strong limitations, it is possible to arrange 3m+3k of these weak entities in R^m to simulate the behavior of a stronger robot that is rigid (i.e., it always reaches its destination) and is endowed with k registers of persistent memory, each of which can store a real number. We call this arrangement a TuringMobile. In its simplest form, a TuringMobile consisting of only three robots can travel in the plane and store and update a single real number. We also prove that this task is impossible with fewer than three robots.
Among the applications of the TuringMobile, we focused on Near-Gathering (all robots have to gather in a small-enough disk) and Pattern Formation (of which Gathering is a special case) with limited visibility. Interestingly, our investigation implies that both problems are solvable in Euclidean spaces of any dimension, even if the visibility graph of the robots is initially disconnected, provided that a small amount of these robots are arranged to form a TuringMobile. In the special case of the plane, a basic TuringMobile of only three robots is sufficient.
Mobile Robots
Turing Machine
Real RAM
Computing methodologies~Multi-agent planning
19:1-19:18
Regular Paper
https://arxiv.org/pdf/1709.08800
Giuseppe A.
Di Luna
Giuseppe A. Di Luna
Aix-Marseille University and LiS Laboratory, Marseille, France
Paola
Flocchini
Paola Flocchini
University of Ottawa, Ottawa, Canada
Nicola
Santoro
Nicola Santoro
Carleton University, Ottawa, Canada
Giovanni
Viglietta
Giovanni Viglietta
JAIST, Nomi City, Japan
10.4230/LIPIcs.DISC.2018.19
C. Agathangelou, C. Georgiou, and M. Mavronicolas. A distributed algorithm for gathering many fat mobile robots in the plane. In 32nd ACM Symposium on Principles of Distributed Computing (PODC), pages 250-259, 2013.
N. Agmon and D. Peleg. Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM Journal on Computing, 36(1):56-82, 2006.
A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Massachusetts, 1974.
H. Ando, Y. Oasa, I. Suzuki, and M. Yamashita. Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transactions on Robotics and Automation, 15(5):818-838, 1999.
Q. Bramas and S. Tixeuil. The random bit complexity of mobile robots scattering. International Journal of Foundations of Computer Science, 28(2):111-134, 2017.
D. Canepa, X. Défago, T. Izumi, and M. Potop-Butucaru. Flocking with oblivious robots. In 18th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), pages 94-108, 2016.
S. Cicerone, G. Di Stefano, and A. Navarra. Minimum-traveled-distance gathering of oblivious robots over given meeting points. In 10th International Symposium on Algorithms and Experiments for Sensor Systems (Algosensors), pages 57-72, 2014.
S. Cicerone, G. Di Stefano, and A. Navarra. Asynchronous pattern formation: The effects of a rigorous approach. In arXiv:1706.02474, 2017.
M. Cieliebak, P. Flocchini, G. Prencipe, and N. Santoro. Distributed computing by mobile robots: Gathering. SIAM Journal on Computing, 41(2):829-879, 2012.
R. Cohen and D. Peleg. Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM Journal on Computing, 36(6):1516-1528, 2005.
P. Courtieu, L. Rieg, S. Tixeuil, and X. Urbain. Impossibility of gathering, a certification. Information Processing Letters, 115(3):447-452, 2015.
P. Courtieu, L. Rieg, S. Tixeuil, and X. Urbain. Certified universal gathering in ℝ² for oblivious mobile robots. In 30th International Symposium on Distributed Computing (DISC), pages 187-200, 2016.
S. Das, P. Flocchini, N. Santoro, and M. Yamashita. Forming sequences of geometric patterns with oblivious mobile robots. Information Processing Letters, 28(2):131-145, 2015.
X. Défago, M. Gradinariu, S. Messika, P. Raipin-Parvédy, and S. Dolev. Fault-tolerant and self-stabilizing mobile robots gathering. In 20th International Symposium on Distributed Computing (DISC), pages 46-60, 2006.
B. Degener, B. Kempkes, P. Kling, and F. Meyer auf der Heide. Linear and competitive strategies for continuous robot formation problems. ACM Transactions on Parallel Computing, 2(1):2:1-2:8, 2015.
B. Degener, B. Kempkes, P. Kling, F. Meyer auf der Heide, P. Pietrzyk, and R. Wattenhofer. A tight runtime bound for synchronous gathering of autonomous robots with limited visibility. In 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 139-148, 2011.
G. Di Luna, P. Flocchini, N. Santoro, and G. Viglietta. Turingmobile: A turing machine of oblivious mobile robots with limited visibility and its applications. In arXiv:1709.08800, 2017.
P. Flocchini, G. Prencipe, and N. Santoro. Distributed Computing by Oblivious Mobile Robots. Morgan &Claypool, 2012.
P. Flocchini, G. Prencipe, N. Santoro, and G. Viglietta. Distributed computing by mobile robots: Uniform circle formation. Distributed Computing, 30(6):413-457, 2017.
P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Gathering of asynchronous robots with limited visibility. Theoretical Computer Science, 337(1-3):147-168, 2005.
P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theoretical Computer Science, 407(1-3):412-447, 2008.
N. Fujinaga, Y. Yamauchi, S. Kijima, and M. Yamahista. Pattern formation by oblivious asynchronous mobile robots. SIAM Journal on Computing, 44(3):740-785, 2015.
T. Izumi, M. Gradinariu, and S. Tixeuil. Connectivity-preserving scattering of mobile robots with limited visibility. In 12th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), pages 319-331, 2010.
P. Linda, G. Prencipe, and G. Viglietta. Getting close without touching: Near-gathering for autonomous mobile robots. Distributed Computing, 28(5):333-349, 2015.
F.P. Preparata and M.I. Shamos. Computational Geometry. Springer-Verlag, Berlin and New York, 1985.
M.I. Shamos. Computational Geometry. Ph.D. thesis, Department of Computer Science, Yale University, 1978.
I. Suzuki and M. Yamashita. Distributed anonymous mobile robots: Formation of geometric patterns. SIAM Journal on Computing, 28(4):1347-1363, 1999.
M. Yamashita and I. Suzuki. Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theoretical Computer Science, 411(26-28):2433-2453, 2010.
Y. Yamauchi, T. Uehara, S. Kijima, and M. Yamashita. Plane formation by synchronous mobile robots in the three-dimensional euclidean space. Journal of the ACM, 64(3):16:1-16:43, 2017.
Giuseppe A. Di Luna, Paola Flocchini, Nicola Santoro, and Giovanni Viglietta
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Beeping a Deterministic Time-Optimal Leader Election
The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we solve the leader election problem with an asymptotically optimal round complexity of O(D + log n), for a network of unknown size n and unknown diameter D (but with unique identifiers). Contrary to the best previously known algorithms in the same setting, the proposed one is deterministic. The techniques we introduce give a new insight as to how local constraints on the exchangeable messages can result in efficient algorithms, when dealing with the beeping model.
Using this deterministic leader election algorithm, we obtain a randomized leader election algorithm for anonymous networks with an asymptotically optimal round complexity of O(D + log n) w.h.p. In previous works this complexity was obtained in expectation only.
Moreover, using deterministic leader election, we obtain efficient algorithms for symmetry-breaking and communication procedures: O(log n) time MIS and 5-coloring for tree networks (which is time-optimal), as well as k-source multi-broadcast for general graphs in O(min(k,log n) * D + k log{(n M)/k}) rounds (for messages in {1,..., M}). This latter result improves on previous solutions when the number of sources k is sublogarithmic (k = o(log n)).
distributed algorithms
leader election
beeping model
time complexity
deterministic algorithms
wireless networks
Theory of computation~Distributed computing models
Theory of computation~Distributed algorithms
Theory of computation~Design and analysis of algorithms
20:1-20:17
Regular Paper
A full version is available at https://hal.archives-ouvertes.fr/hal-01794711.
Fabien
Dufoulon
Fabien Dufoulon
LRI, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France
https://orcid.org/0000-0003-2977-4109
Janna
Burman
Janna Burman
LRI, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France
Joffroy
Beauquier
Joffroy Beauquier
LRI, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France
10.4230/LIPIcs.DISC.2018.20
Y. Afek, N. Alon, Z. Bar-Joseph, A. Cornejo, B. Haeupler, and F. Kuhn. Beeping a maximal independent set. Distributed Computing, 26(4):195-208, Aug 2013.
D. Alistarh, A. Cornejo, M. Ghaffari, and N. Lynch. Firefly synchronization with asynchronous wake-up. In Workshop on Biological Distributed Algorithms, 2014.
J. Beauquier, J. Burman, F. Dufoulon, and S. Kutten. Fast Beeping Protocols for Deterministic MIS and (Δ+1)-Coloring in Sparse Graphs. In IEEE INFOCOM, 2018, to appear.
A. Casteigts, Y. Métivier, J. M. Robson, and A. Zemmari. Design Patterns in Beeping Algorithms. In OPODIS, pages 15:1-15:16, 2016.
A. Casteigts, Y. Métivier, J.M. Robson, and A. Zemmari. Deterministic leader election in 𝒪(D+ logn) time with messages of size 𝒪(1). In DISC, pages 16-28, 2016.
I. Chlamtac and S. Kutten. On broadcasting in radio networks - problem analysis and protocol design. IEEE Transactions on Communications, 33(12):1240-1246, 1985.
A. Cornejo and F. Kuhn. Deploying wireless networks with beeps. In DISC, pages 148-162, 2010.
A. Czumaj and P. Davies. Optimal leader election in multi-hop radio networks. ArXiv e-prints, 2015. URL: http://arxiv.org/abs/1505.06149.
http://arxiv.org/abs/1505.06149
A. Czumaj and P. Davies. Brief announcement: Optimal leader election in multi-hop radio networks. In PODC, pages 47-49, 2016.
A. Czumaj and P. Davies. Communicating with Beeps. In OPODIS, pages 1-16, 2016.
Y. Dinitz and N. Solomon. Two absolute bounds for distributed bit complexity. In Structural Information and Communication Complexity, pages 115-126, 2005.
K.-T. Förster, J. Seidel, and R. Wattenhofer. Deterministic leader election in multi-hop beeping networks. In DISC, pages 212-226, 2014.
M. Ghaffari and B. Haeupler. Near optimal leader election in multi-hop radio networks. In SODA, pages 748-766, 2013.
S. Gilbert and C. Newport. The computational power of beeps. In DISC, pages 31-46, 2015.
R. Guerraoui and A. Maurer. Byzantine fireflies. In DISC, pages 47-59, 2015.
S. Kutten, G. Pandurangan, D. Peleg, P. Robinson, and A. Trehan. On the complexity of universal leader election. In PODC, pages 100-109, 2013.
Y. Métivier, J.M. Robson, and A. Zemmari. Analysis of fully distributed splitting and naming probabilistic procedures and applications. Theoretical Computer Science, 584:115-130, 2015. Special Issue on Structural Information and Communication Complexity.
K. Nakano and S. Olariu. Randomized o(log log n)-round leader election protocols in packet radio networks. In Algorithms and Computation, pages 210-219, 1998.
S. Navlakha and Z. Bar-Joseph. Distributed information processing in biological and computational systems. Commun. ACM, 58(1):94-102, 2014.
D. Peleg. Time-efficient broadcasting in radio networks: A review. In Distributed Computing and Internet Technology, pages 1-18, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg.
J. Schneider and R. Wattenhofer. What is the use of collision detection (in wireless networks)? In DISC, pages 133-147, 2010.
A. Scott, P. Jeavons, and L. Xu. Feedback from nature: An optimal distributed algorithm for maximal independent set selection. In PODC, pages 147-156, 2013.
J. Seidel. Anonymous distributed computing: computability, randomization and checkability. PhD thesis, ETH Zurich, Zürich, Switzerland, 2015. URL: http://d-nb.info/1080812695.
http://d-nb.info/1080812695
Fabien Dufoulon, Janna Burman, and Joffroy Beauquier
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
An Almost Tight RMR Lower Bound for Abortable Test-And-Set
We prove a lower bound of Omega(log n/log log n) for the remote memory reference (RMR) complexity of abortable test-and-set (leader election) in the cache-coherent (CC) and the distributed shared memory (DSM) model. This separates the complexities of abortable and non-abortable test-and-set, as the latter has constant RMR complexity [Wojciech Golab et al., 2010].
Golab, Hendler, Hadzilacos and Woelfel [Wojciech M. Golab et al., 2012] showed that compare-and-swap can be implemented from registers and test-and-set objects with constant RMR complexity. We observe that a small modification to that implementation is abortable, provided that the used test-and-set objects are atomic (or abortable). As a consequence, using existing efficient randomized wait-free implementations of test-and-set [George Giakkoupis and Philipp Woelfel, 2012], we obtain randomized abortable compare-and-swap objects with almost constant (O(log^* n)) RMR complexity.
Abortability
Test-And-Set
Leader Election
Compare-and-Swap
RMR Complexity
Lower Bound
Theory of computation~Shared memory algorithms
21:1-21:19
Regular Paper
This research was undertaken, in part, thanks to funding from the Canada Research Chairs program and from the Discovery Grants program of the Natural Sciences and Engineering Research Council of Canada (NSERC).
https://arxiv.org/abs/1805.04840
Aryaz
Eghbali
Aryaz Eghbali
Department of Computer Science, University of Calgary, Canada
Philipp
Woelfel
Philipp Woelfel
Department of Computer Science, University of Calgary, Canada
10.4230/LIPIcs.DISC.2018.21
Zahra Aghazadeh, Wojciech Golab, and Philipp Woelfel. Making objects writable. In \PODC33rd, pages 385-395, 2014. URL: http://dx.doi.org/10.1145/2611462.2611483.
http://dx.doi.org/10.1145/2611462.2611483
Zahra Aghazadeh and Philipp Woelfel. Space- and time-efficient long-lived test-and-set objects. In ØPODIS18th, pages 404-419, 2014. URL: http://dx.doi.org/10.1007/978-3-319-14472-6_27.
http://dx.doi.org/10.1007/978-3-319-14472-6_27
Zahra Aghazadeh and Philipp Woelfel. Upper bounds for boundless tagging with bounded objects. In \DISC30th, pages 442-457, 2016. URL: http://dx.doi.org/10.1007/978-3-662-53426-7_32.
http://dx.doi.org/10.1007/978-3-662-53426-7_32
Marcos Aguilera, Svend Frølund, Vassos Hadzilacos, Stephanie Lorraine Horn, and Sam Toueg. Abortable and query-abortable objects and their efficient implementation. In \PODC26th, pages 23-32, 2007.
Dan Alistarh and James Aspnes. Sub-logarithmic test-and-set against a weak adversary. In \DISC25th, pages 97-109, 2011.
Dan Alistarh, James Aspnes, Keren Censor-Hillel, Seth Gilbert, and Morteza Zadimoghaddam. Optimal-time adaptive strong renaming, with applications to counting. In \PODC30th, pages 239-248, 2011.
Dan Alistarh, James Aspnes, Seth Gilbert, and Rachid Guerraoui. The complexity of renaming. In \FOCS52nd, pages 718-727, 2011. URL: http://dx.doi.org/10.1109/FOCS.2011.66.
http://dx.doi.org/10.1109/FOCS.2011.66
Dan Alistarh, Hagit Attiya, Seth Gilbert, Andrei Giurgiu, and Rachid Guerraoui. Fast randomized test-and-set and renaming. In \DISC24th, pages 94-108, 2010.
James H. Anderson and Yong-Jik Kim. Adaptive mutual exclusion with local spinning. In \DISC14th, pages 29-43, 2000.
James H. Anderson and Yong-Jik Kim. An improved lower bound for the time complexity of mutual exclusion. \DistComp, 15:221-253, 2002.
T. Anderson. The performance of spin lock alternatives for shared-memory multiprocessors. IEEE Transactions on Parallel and Distributed Systems, 1:6-16, 1990.
Hagit Attiya, Rachid Guerraoui, Danny Hendler, and Petr Kuznetsov. The complexity of obstruction-free implementations. \JACM, 56(4):24:1-24:33, 2009. URL: http://dx.doi.org/10.1145/1538902.1538908.
http://dx.doi.org/10.1145/1538902.1538908
Hagit Attiya, Danny Hendler, and Philipp Woelfel. Tight RMR lower bounds for mutual exclusion and other problems. In \STOC40th, pages 217-226, 2008.
Michael Bender and Seth Gilbert. Mutual exclusion with O(log²log n) amortized work. In \FOCS52nd, pages 728-737, 2011.
Harry Buhrman, Alessandro Panconesi, Riccardo Silvestri, and Paul Vitányi. On the importance of having an identity or, is consensus really universal? Distributed Computing, 18(3):167-176, 2006. URL: http://dx.doi.org/10.1007/s00446-005-0121-z.
http://dx.doi.org/10.1007/s00446-005-0121-z
Robert Danek and Wojciech Golab. Closing the complexity gap between FCFS mutual exclusion and mutual exclusion. Distributed Computing, 23(2):87-111, 2010. URL: http://dx.doi.org/10.1007/s00446-010-0096-2.
http://dx.doi.org/10.1007/s00446-010-0096-2
Robert Danek and Hyonho Lee. Brief announcement: Local-spin algorithms for abortable mutual exclusion and related problems. In \DISC22nd, pages 512-513, 2008. URL: http://dx.doi.org/10.1007/978-3-540-87779-0_41.
http://dx.doi.org/10.1007/978-3-540-87779-0_41
E. W. Dijkstra. Solution of a problem in concurrent programming control. Communications of the ACM, 8:569, 1965.
Cynthia Dwork, Maurice Herlihy, and Orli Waarts. Contention in shared memory algorithms. \JACM, 44(6):779-805, 1997. URL: http://dx.doi.org/10.1145/268999.269000.
http://dx.doi.org/10.1145/268999.269000
Wayne Eberly, Lisa Higham, and Jolanta Warpechowska-Gruca. Long-lived, fast, waitfree renaming with optimal name space and high throughput. In \DISC12th, pages 149-160, 1998.
Aryaz Eghbali and Philipp Woelfel. An almost tight RMR lower bound for abortable test-and-set. CoRR, abs/1805.04840, 2018. URL: http://arxiv.org/abs/1805.04840.
http://arxiv.org/abs/1805.04840
Michael J. Fischer, Nancy A. Lynch, and Mike Paterson. Impossibility of distributed consensus with one faulty process. \JACM, 32(2):374-382, 1985. URL: http://dx.doi.org/10.1145/3149.214121.
http://dx.doi.org/10.1145/3149.214121
George Giakkoupis and Philipp Woelfel. On the time and space complexity of randomized test-and-set. In \PODC31st, pages 19-28, 2012. URL: http://dx.doi.org/10.1145/2332432.2332436.
http://dx.doi.org/10.1145/2332432.2332436
George Giakkoupis and Philipp Woelfel. A tight RMR lower bound for randomized mutual exclusion. In \STOC44th, pages 983-1002, 2012. URL: http://dx.doi.org/10.1145/2213977.2214066.
http://dx.doi.org/10.1145/2213977.2214066
George Giakkoupis and Philipp Woelfel. Randomized mutual exclusion with constant amortized RMR complexity on the DSM. In \FOCS55nd, 2014. To appear.
George Giakkoupis and Philipp Woelfel. Randomized abortable mutual exclusion with constant amortized RMR complexity on the CC model. In \PODC36th, pages 221-229, 2017. URL: http://dx.doi.org/10.1145/3087801.3087837.
http://dx.doi.org/10.1145/3087801.3087837
Wojciech Golab, Danny Hendler, and Philipp Woelfel. An O(1) RMRs leader election algorithm. \SIAMJC, 39(7):2726-2760, 2010.
Wojciech M. Golab, Vassos Hadzilacos, Danny Hendler, and Philipp Woelfel. Constant-RMR implementations of cas and other synchronization primitives using read and write operations. In \PODC26th, pages 3-12, 2007.
Wojciech M. Golab, Vassos Hadzilacos, Danny Hendler, and Philipp Woelfel. RMR-efficient implementations of comparison primitives using read and write operations. \DistComp, 25(2):109-162, 2012. URL: http://dx.doi.org/10.1007/s00446-011-0150-8.
http://dx.doi.org/10.1007/s00446-011-0150-8
Danny Hendler and Philipp Woelfel. Randomized mutual exclusion in O(log N/log log N) RMRs. In \PODC28th, pages 26-35, 2009.
Danny Hendler and Philipp Woelfel. Adaptive randomized mutual exclusion in sub-logarithmic expected time. In \PODC29th, pages 141-150, 2010.
Danny Hendler and Philipp Woelfel. Randomized mutual exclusion with sub-logarithmic RMR-complexity. \DistComp, 24(1):3-19, 2011. URL: http://dx.doi.org/10.1007/s00446-011-0128-6.
http://dx.doi.org/10.1007/s00446-011-0128-6
Prasad Jayanti. Adaptive and efficient abortable mutual exclusion. In \PODC22nd, pages 295-304, 2003. URL: http://dx.doi.org/10.1145/872035.872079.
http://dx.doi.org/10.1145/872035.872079
Prasad Jayanti, Srdjan Petrovic, and Neha Narula. Read/write based fast-path transformation for FCFS mutual exclusion. In \SOFSEM31st, pages 209-218, 2005.
Y.-J. Kim and J. Anderson. A time complexity bound for adaptive mutual exclusion. In \DISC15th, pages 1-15, 2001.
Yong-Jik Kim and James H. Anderson. Nonatomic mutual exclusion with local spinning. \DistComp, 19(1):19-61, 2006. URL: http://dx.doi.org/10.1007/s00446-006-0003-z.
http://dx.doi.org/10.1007/s00446-006-0003-z
Clyde P. Kruskal, Larry Rudolph, and Marc Snir. Efficient synchronization on multiprocessors with shared memory. \TOPLAS, 10(4):579-601, 1988. URL: http://dx.doi.org/10.1145/48022.48024.
http://dx.doi.org/10.1145/48022.48024
Hyonho Lee. Transformations of mutual exclusion algorithms from the cache-coherent model to the distributed shared memory model. In \ICDCS25th, pages 261-270, 2005. URL: http://dx.doi.org/10.1109/ICDCS.2005.83.
http://dx.doi.org/10.1109/ICDCS.2005.83
Hyonho Lee. Fast local-spin abortable mutual exclusion with bounded space. In ØPODIS14th, pages 364-379, 2010. URL: http://dx.doi.org/10.1007/978-3-642-17653-1_27.
http://dx.doi.org/10.1007/978-3-642-17653-1_27
Hyonho Lee. Local-spin Abortable Mutual Exclusion. PhD thesis, University of Toronto, 2011.
Alessandro Panconesi, Marina Papatriantafilou, Philippas Tsigas, and Paul M. B. Vitányi. Randomized naming using wait-free shared variables. Distributed Computing, 11(3):113-124, 1998.
Abhijeet Pareek and Philipp Woelfel. RMR-efficient randomized abortable mutual exclusion. In \DISC26th, pages 267-281, 2012. URL: http://dx.doi.org/10.1007/978-3-642-33651-5_19.
http://dx.doi.org/10.1007/978-3-642-33651-5_19
Michael L Scott. Non-blocking timeout in scalable queue-based spin locks. In Proceedings of the twenty-first annual symposium on Principles of distributed computing, pages 31-40. ACM, 2002.
Paul Turán. Eine extremalaufgabe aus der graphentheorie. Mat. Fiz. Lapok, 48(436-452):61, 1941.
Aryaz Eghbali and Philipp Woelfel
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Distributed Set Cover Approximation: Primal-Dual with Optimal Locality
This paper presents a deterministic distributed algorithm for computing an f(1+epsilon) approximation of the well-studied minimum set cover problem, for any constant epsilon>0, in O(log (f Delta)/log log (f Delta)) rounds. Here, f denotes the maximum element frequency and Delta denotes the cardinality of the largest set. This f(1+epsilon) approximation almost matches the f-approximation guarantee of standard centralized primal-dual algorithms, which is known to be essentially the best possible approximation for polynomial-time computations. The round complexity almost matches the Omega(log (Delta)/log log (Delta)) lower bound of Kuhn, Moscibroda, Wattenhofer [JACM'16], which holds for even f=2 and for any poly(log Delta) approximation. Our algorithm also gives an alternative way to reproduce the time-optimal 2(1+epsilon)-approximation of vertex cover, with round complexity O(log Delta/log log Delta), as presented by Bar-Yehuda, Censor-Hillel, and Schwartzman [PODC'17] for weighted vertex cover. Our method is quite different and it can be viewed as a locality-optimal way of performing primal-dual for the more general case of set cover. We note that the vertex cover algorithm of Bar-Yehuda et al. does not extend to set cover (when f >= 3).
Distributed Algorithms
Approximation Algorithms
Set Cover
Vertex Cover
Theory of computation~Graph algorithms analysis
Mathematics of computing~Graph algorithms
Theory of computation~Distributed algorithms
22:1-22:14
Regular Paper
Guy
Even
Guy Even
Tel-Aviv University, Israel
Mohsen
Ghaffari
Mohsen Ghaffari
ETH Zurich, Switzerland
Moti
Medina
Moti Medina
Ben-Gurion University, Israel
https://orcid.org/0000-0002-5572-3754
10.4230/LIPIcs.DISC.2018.22
Matti Åstrand and Jukka Suomela. Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks. In Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures, pages 294-302. ACM, 2010.
Reuven Bar-Yehuda, Keren Censor-Hillel, Mohsen Ghaffari, and Gregory Schwartzman. Distributed approximation of maximum independent set and maximum matching. In Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2017, Washington, DC, USA, July 25-27, 2017, pages 165-174, 2017. URL: http://dx.doi.org/10.1145/3087801.3087806.
http://dx.doi.org/10.1145/3087801.3087806
Reuven Bar-Yehuda, Keren Censor-Hillel, and Gregory Schwartzman. A Distributed (2+ε)-Approximation for Vertex Cover in O(log Δ/ ε log logΔ) Rounds. J. ACM, 64(3):23:1-23:11, 2017. URL: http://dx.doi.org/10.1145/3060294.
http://dx.doi.org/10.1145/3060294
Reuven Bar-Yehuda and Shimon Even. A linear-time approximation algorithm for the weighted vertex cover problem. Journal of Algorithms, 2(2):198-203, 1981.
Reuven Bar-Yehuda and Shimon Even. A local-ratio theorem for approximating the weighted vertex cover problem. Technion-Israel Institute of Technology. Department of Computer Science, 1983.
Reuven Bar-Yehuda and Dror Rawitz. On the equivalence between the primal-dual schema and the local ratio technique. SIAM Journal on Discrete Mathematics, 19(3):762-797, 2005.
R. Ben-Basat, G. Even, K. Kawarabayashi, and G. Schwartzman. A Deterministic Distributed 2-Approximation for Weighted Vertex Cover in O(log nlogΔ / log²logΔ) Rounds. ArXiv e-prints (Appeared in SIROCCO 2018), 2018. URL: http://arxiv.org/abs/1804.01308.
http://arxiv.org/abs/1804.01308
Irit Dinur, Venkatesan Guruswami, Subhash Khot, and Oded Regev. A new multilayered pcp and the hardness of hypergraph vertex cover. SIAM Journal on Computing, 34(5):1129-1146, 2005.
Irit Dinur and Samuel Safra. On the hardness of approximating minimum vertex cover. Annals of mathematics, pages 439-485, 2005.
Uriel Feige. A threshold of ln n for approximating set cover. Journal of the ACM (JACM), 45(4):634-652, 1998.
Mohsen Ghaffari. An improved distributed algorithm for maximal independent set. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, Arlington, VA, USA, January 10-12, 2016, pages 270-277, 2016. URL: http://dx.doi.org/10.1137/1.9781611974331.ch20.
http://dx.doi.org/10.1137/1.9781611974331.ch20
Mohsen Ghaffari, David G Harris, and Fabian Kuhn. On derandomizing local distributed algorithms. arXiv preprint arXiv:1711.02194, 2017.
Mohsen Ghaffari, Fabian Kuhn, and Yannic Maus. On the complexity of local distributed graph problems. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages 784-797. ACM, 2017.
Johan Håstad. Some optimal inapproximability results. Journal of the ACM (JACM), 48(4):798-859, 2001.
Jonas Holmerin. Improved inapproximability results for vertex cover on k-uniform hypergraphs. In International Colloquium on Automata, Languages, and Programming, pages 1005-1016. Springer, 2002.
Subhash Khot and Oded Regev. Vertex cover might be hard to approximate to within 2-ε. Journal of Computer and System Sciences, 74(3):335-349, 2008.
Christos Koufogiannakis and Neal E Young. Distributed algorithms for covering, packing and maximum weighted matching. Distributed Computing, 24(1):45-63, 2011.
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. The price of being near-sighted. In Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pages 980-989. Society for Industrial and Applied Mathematics, 2006.
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. Local computation: Lower and upper bounds. J. ACM, 63(2):17:1-17:44, 2016. URL: http://dx.doi.org/10.1145/2742012.
http://dx.doi.org/10.1145/2742012
Nathan Linial. Distributive graph algorithms global solutions from local data. In Foundations of Computer Science, 1987., 28th Annual Symposium on, pages 331-335. IEEE, 1987.
Carsten Lund and Mihalis Yannakakis. On the hardness of approximating minimization problems. Journal of the ACM (JACM), 41(5):960-981, 1994.
Dana Moshkovitz. The projection games conjecture and the np-hardness of ln n-approximating set-cover. Theory of Computing, 11:221-235, 2015. URL: http://dx.doi.org/10.4086/toc.2015.v011a007.
http://dx.doi.org/10.4086/toc.2015.v011a007
David Peleg. Distributed computing: a locality-sensitive approach. SIAM, 2000.
Jukka Suomela. Survey of local algorithms. ACM Computing Surveys (CSUR), 45(2):24, 2013.
Luca Trevisan. Non-approximability results for optimization problems on bounded degree instances. In Proceedings of the thirty-third annual ACM symposium on Theory of computing, pages 453-461. ACM, 2001.
Vijay V Vazirani. Approximation algorithms. Springer Science &Business Media, 2013.
David P Williamson and David B Shmoys. The design of approximation algorithms. Cambridge university press, 2011.
Guy Even, Mohsen Ghaffari, and Moti Medina
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Order out of Chaos: Proving Linearizability Using Local Views
Proving the linearizability of highly concurrent data structures, such as those using optimistic concurrency control, is a challenging task. The main difficulty is in reasoning about the view of the memory obtained by the threads, because as they execute, threads observe different fragments of memory from different points in time. Until today, every linearizability proof has tackled this challenge from scratch.
We present a unifying proof argument for the correctness of unsynchronized traversals, and apply it to prove the linearizability of several highly concurrent search data structures, including an optimistic self-balancing binary search tree, the Lazy List and a lock-free skip list. Our framework harnesses sequential reasoning about the view of a thread, considering the thread as if it traverses the data structure without interference from other operations. Our key contribution is showing that properties of reachability along search paths can be deduced for concurrent traversals from such interference-free traversals, when certain intuitive conditions are met. Basing the correctness of traversals on such local view arguments greatly simplifies linearizability proofs. At the heart of our result lies a notion of order on the memory, corresponding to the order in which locations in memory are read by the threads, which guarantees a certain notion of consistency between the view of the thread and the actual memory.
To apply our framework, the user proves that the data structure satisfies two conditions: (1) acyclicity of the order on memory, even when it is considered across intermediate memory states, and (2) preservation of search paths to locations modified by interfering writes. Establishing the conditions, as well as the full linearizability proof utilizing our proof argument, reduces to simple concurrent reasoning. The result is a clear and comprehensible correctness proof, and elucidates common patterns underlying several existing data structures.
concurrency and synchronization
concurrent data structures
lineariazability
optimistic concurrency control
verification and formal methods
Computing methodologies~Shared memory algorithms
Theory of computation~Program verification
23:1-23:21
Regular Paper
https://arxiv.org/abs/1805.03992
Yotam M. Y.
Feldman
Yotam M. Y. Feldman
Tel Aviv University, Israel
Constantin
Enea
Constantin Enea
IRIF, Univ. Paris Diderot & CNRS, France
Adam
Morrison
Adam Morrison
Tel Aviv University, Israel
Noam
Rinetzky
Noam Rinetzky
Tel Aviv University, Israel
Sharon
Shoham
Sharon Shoham
Tel Aviv University, Israel
10.4230/LIPIcs.DISC.2018.23
Parosh Aziz Abdulla, Frédéric Haziza, Lukás Holík, Bengt Jonsson, and Ahmed Rezine. An integrated specification and verification technique for highly concurrent data structures. In TACAS, pages 324-338, 2013. URL: http://dx.doi.org/10.1007/978-3-642-36742-7_23.
http://dx.doi.org/10.1007/978-3-642-36742-7_23
Daphna Amit, Noam Rinetzky, Thomas W. Reps, Mooly Sagiv, and Eran Yahav. Comparison under abstraction for verifying linearizability. In CAV '07, volume 4590 of LNCS, pages 477-490, 2007. URL: http://dx.doi.org/10.1007/978-3-540-73368-3_49.
http://dx.doi.org/10.1007/978-3-540-73368-3_49
Maya Arbel and Hagit Attiya. Concurrent Updates with RCU: Search Tree As an Example. In Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing, PODC '14, pages 196-205, New York, NY, USA, 2014. ACM. URL: http://dx.doi.org/10.1145/2611462.2611471.
http://dx.doi.org/10.1145/2611462.2611471
Richard Bornat, Cristiano Calcagno, Peter W. O'Hearn, and Matthew J. Parkinson. Permission accounting in separation logic. In Jens Palsberg and Martín Abadi, editors, Proceedings of the 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2005, Long Beach, California, USA, January 12-14, 2005, pages 259-270. ACM, 2005. URL: http://dx.doi.org/10.1145/1040305.1040327.
http://dx.doi.org/10.1145/1040305.1040327
Ahmed Bouajjani, Michael Emmi, Constantin Enea, and Jad Hamza. Verifying concurrent programs against sequential specifications. In ESOP '13, volume 7792 of LNCS, pages 290-309. Springer, 2013.
Ahmed Bouajjani, Michael Emmi, Constantin Enea, and Jad Hamza. On reducing linearizability to state reachability. In Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part II, pages 95-107, 2015.
Ahmed Bouajjani, Michael Emmi, Constantin Enea, and Suha Orhun Mutluergil. Proving linearizability using forward simulations. In Rupak Majumdar and Viktor Kuncak, editors, Computer Aided Verification - 29th International Conference, CAV 2017, Heidelberg, Germany, July 24-28, 2017, Proceedings, Part II, volume 10427 of Lecture Notes in Computer Science, pages 542-563. Springer, 2017. URL: http://dx.doi.org/10.1007/978-3-319-63390-9_28.
http://dx.doi.org/10.1007/978-3-319-63390-9_28
Nathan Grasso Bronson, Jared Casper, Hassan Chafi, and Kunle Olukotun. A practical concurrent binary search tree. In Proceedings of the 15th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPOPP 2010, Bangalore, India, January 9-14, 2010, pages 257-268, 2010.
Stephen D. Brookes. A semantics for concurrent separation logic. In CONCUR 2004 - Concurrency Theory, 15th International Conference, London, UK, August 31 - September 3, 2004, Proceedings, pages 16-34, 2004. URL: http://dx.doi.org/10.1007/978-3-540-28644-8_2.
http://dx.doi.org/10.1007/978-3-540-28644-8_2
Trevor Brown, Faith Ellen, and Eric Ruppert. A general technique for non-blocking trees. In PPoPP, 2014.
Austin T. Clements, M. Frans Kaashoek, and Nickolai Zeldovich. Scalable address spaces using RCU balanced trees. In ASPLOS, 2012.
Tyler Crain, Vincent Gramoli, and Michel Raynal. A contention-friendly binary search tree. In Felix Wolf, Bernd Mohr, and Dieter an Mey, editors, Euro-Par 2013 Parallel Processing, pages 229-240, Berlin, Heidelberg, 2013. Springer Berlin Heidelberg.
Tyler Crain, Vincent Gramoli, and Michel Raynal. No Hot Spot Non-blocking Skip List. In ICDCS, 2013.
Tyler Crain, Vincent Gramoli, and Michel Raynal. A fast contention-friendly binary search tree. Parallel Processing Letters, 26(03):1650015, 2016. URL: http://dx.doi.org/10.1142/S0129626416500158.
http://dx.doi.org/10.1142/S0129626416500158
Pedro da Rocha Pinto, Thomas Dinsdale-Young, and Philippa Gardner. Tada: A logic for time and data abstraction. In Richard E. Jones, editor, ECOOP 2014 - Object-Oriented Programming - 28th European Conference, Uppsala, Sweden, July 28 - August 1, 2014. Proceedings, volume 8586 of Lecture Notes in Computer Science, pages 207-231. Springer, 2014. URL: http://dx.doi.org/10.1007/978-3-662-44202-9_9.
http://dx.doi.org/10.1007/978-3-662-44202-9_9
Tudor David, Rachid Guerraoui, and Vasileios Trigonakis. Asynchronized Concurrency: The Secret to Scaling Concurrent Search Data Structures. In ASPLOS, 2015.
Dana Drachsler, Martin Vechev, and Eran Yahav. Practical Concurrent Binary Search Trees via Logical Ordering. In PPoPP, 2014.
Cezara Dragoi, Ashutosh Gupta, and Thomas A. Henzinger. Automatic linearizability proofs of concurrent objects with cooperating updates. In CAV '13, volume 8044 of LNCS, pages 174-190. Springer, 2013. URL: http://dx.doi.org/10.1007/978-3-642-39799-8_11.
http://dx.doi.org/10.1007/978-3-642-39799-8_11
Faith Ellen, Panagiota Fatourou, Eric Ruppert, and Franck van Breugel. Non-blocking Binary Search Trees. In PODC, 2010.
Yotam M. Y. Feldman, Constantin Enea, Adam Morrison, Noam Rinetzky, and Sharon Shoham. Order out of chaos: Proving linearizability using local views. CoRR, abs/1805.03992, 2018. URL: http://arxiv.org/abs/1805.03992.
http://arxiv.org/abs/1805.03992
Keir Fraser. Practical lock-freedom. PhD thesis, University of Cambridge, Computer Laboratory, University of Cambridge, Computer Laboratory, February 2004.
Timothy L. Harris. A Pragmatic Implementation of Non-blocking Linked-Lists. In DISC, 2001.
Steve Heller, Maurice Herlihy, Victor Luchangco, Mark Moir, Bill Scherer, and Nir Shavit. A lazy concurrent list-based set algorithm. In OPODIS, 2005.
Thomas A. Henzinger, Ali Sezgin, and Viktor Vafeiadis. Aspect-oriented linearizability proofs. In CONCUR, pages 242-256, 2013. URL: http://dx.doi.org/10.1007/978-3-642-40184-8_18.
http://dx.doi.org/10.1007/978-3-642-40184-8_18
M. P. Herlihy and J. M. Wing. Linearizability: a correctness condition for concurrent objects. TOPLAS, 12(3), 1990.
Maurice Herlihy, Yossi Lev, Victor Luchangco, and Nir Shavit. A Simple Optimistic Skiplist Algorithm. In SIROCCO, 2007.
Maurice Herlihy and Nir Shavit. The Art of Multiprocessor Programming. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2008.
Shane V. Howley and Jeremy Jones. A Non-blocking Internal Binary Search Tree. In SPAA, 2012.
Cliff B. Jones. Specification and design of (parallel) programs. In IFIP Congress, pages 321-332, 1983.
Ralf Jung, David Swasey, Filip Sieczkowski, Kasper Svendsen, Aaron Turon, Lars Birkedal, and Derek Dreyer. Iris: Monoids and invariants as an orthogonal basis for concurrent reasoning. In Sriram K. Rajamani and David Walker, editors, Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2015, Mumbai, India, January 15-17, 2015, pages 637-650. ACM, 2015. URL: http://dx.doi.org/10.1145/2676726.2676980.
http://dx.doi.org/10.1145/2676726.2676980
Siddharth Krishna, Dennis E. Shasha, and Thomas Wies. Go with the flow: compositional abstractions for concurrent data structures. PACMPL, 2(POPL):37:1-37:31, 2018. URL: http://dx.doi.org/10.1145/3158125.
http://dx.doi.org/10.1145/3158125
Kfir Lev-Ari, Gregory V. Chockler, and Idit Keidar. A constructive approach for proving data structures' linearizability. In Yoram Moses, editor, Distributed Computing - 29th International Symposium, DISC 2015, Tokyo, Japan, October 7-9, 2015, Proceedings, volume 9363 of Lecture Notes in Computer Science, pages 356-370. Springer, 2015. URL: http://dx.doi.org/10.1007/978-3-662-48653-5_24.
http://dx.doi.org/10.1007/978-3-662-48653-5_24
Ruy Ley-Wild and Aleksandar Nanevski. Subjective auxiliary state for coarse-grained concurrency. In Roberto Giacobazzi and Radhia Cousot, editors, The 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL '13, Rome, Italy - January 23 - 25, 2013, pages 561-574. ACM, 2013. URL: http://dx.doi.org/10.1145/2429069.2429134.
http://dx.doi.org/10.1145/2429069.2429134
Hongjin Liang and Xinyu Feng. Modular verification of linearizability with non-fixed linearization points. In ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI '13, Seattle, WA, USA, June 16-19, 2013, pages 459-470, 2013.
Maged M. Michael. High Performance Dynamic Lock-free Hash Tables and List-based Sets. In SPAA, 2002.
Aravind Natarajan and Neeraj Mittal. Fast Concurrent Lock-free Binary Search Trees. In PPoPP, 2014.
P. W. O'Hearn, N. Rinetzky, M. T. Vechev, E. Yahav, and G. Yorsh. Verifying linearizability with hindsight. In 29th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC), pages 85-94, 2010.
Peter W. O'Hearn. Resources, concurrency and local reasoning. In CONCUR 2004 - Concurrency Theory, 15th International Conference, London, UK, August 31 - September 3, 2004, Proceedings, pages 49-67, 2004. URL: http://dx.doi.org/10.1007/978-3-540-28644-8_4.
http://dx.doi.org/10.1007/978-3-540-28644-8_4
Susan S. Owicki and David Gries. Verifying properties of parallel programs: An axiomatic approach. Commun. ACM, 19(5):279-285, 1976. URL: http://dx.doi.org/10.1145/360051.360224.
http://dx.doi.org/10.1145/360051.360224
Matthew J. Parkinson, Richard Bornat, and Peter W. O'Hearn. Modular verification of a non-blocking stack. In Martin Hofmann and Matthias Felleisen, editors, Proceedings of the 34th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2007, Nice, France, January 17-19, 2007, pages 297-302. ACM, 2007. URL: http://dx.doi.org/10.1145/1190216.1190261.
http://dx.doi.org/10.1145/1190216.1190261
Arunmoezhi Ramachandran and Neeraj Mittal. A Fast Lock-Free Internal Binary Search Tree. In ICDCN, 2015.
Ilya Sergey, Aleksandar Nanevski, and Anindya Banerjee. Specifying and verifying concurrent algorithms with histories and subjectivity. In Jan Vitek, editor, Programming Languages and Systems - 24th European Symposium on Programming, ESOP 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015. Proceedings, volume 9032 of Lecture Notes in Computer Science, pages 333-358. Springer, 2015. URL: http://dx.doi.org/10.1007/978-3-662-46669-8_14.
http://dx.doi.org/10.1007/978-3-662-46669-8_14
Dennis E. Shasha and Nathan Goodman. Concurrent search structure algorithms. ACM Trans. Database Syst., 13(1):53-90, 1988. URL: http://dx.doi.org/10.1145/42201.42204.
http://dx.doi.org/10.1145/42201.42204
Joseph R Shoenfield. The problem of predicativity. In Mathematical Logic In The 20th Century, pages 427-434. World Scientific, 2003.
Josh Triplett, Paul E. McKenney, and Jonathan Walpole. Resizable, Scalable, Concurrent Hash Tables via Relativistic Programming. In USENIX ATC, 2011.
Aaron Turon, Derek Dreyer, and Lars Birkedal. Unifying refinement and hoare-style reasoning in a logic for higher-order concurrency. In Greg Morrisett and Tarmo Uustalu, editors, ACM SIGPLAN International Conference on Functional Programming, ICFP'13, Boston, MA, USA - September 25 - 27, 2013, pages 377-390. ACM, 2013. URL: http://dx.doi.org/10.1145/2500365.2500600.
http://dx.doi.org/10.1145/2500365.2500600
V. Vafeiadis. Modular fine-grained concurrency verification. PhD thesis, University of Cambridge, 2008.
V. Vafeiadis, M. Herlihy, T. Hoare, and M. Shapiro. Proving correctness of highly-concurrent linearisable objects. In PPoPP, 2006.
Viktor Vafeiadis. Shape-value abstraction for verifying linearizability. In VMCAI '09: Proc. 10th Intl. Conf. on Verification, Model Checking, and Abstract Interpretation, volume 5403 of LNCS, pages 335-348. Springer, 2009. URL: http://dx.doi.org/10.1007/978-3-540-93900-9_27.
http://dx.doi.org/10.1007/978-3-540-93900-9_27
Viktor Vafeiadis. Automatically proving linearizability. In CAV '10, volume 6174 of LNCS, pages 450-464, 2010. URL: http://dx.doi.org/10.1007/978-3-642-14295-6_40.
http://dx.doi.org/10.1007/978-3-642-14295-6_40
Viktor Vafeiadis, Maurice Herlihy, Tony Hoare, and Marc Shapiro. Proving correctness of highly-concurrent linearisable objects. In PPOPP '06, pages 129-136. ACM, 2006. URL: http://dx.doi.org/10.1145/1122971.1122992.
http://dx.doi.org/10.1145/1122971.1122992
Viktor Vafeiadis, Maurice Herlihy, Tony Hoare, and Marc Shapiro. A safety proof of a lazy concurrent list-based set implementation. Technical Report UCAM-CL-TR-659, University of Cambridge, Computer Laboratory, 2006.
He Zhu, Gustavo Petri, and Suresh Jagannathan. Poling: SMT aided linearizability proofs. In Computer Aided Verification - 27th International Conference, CAV 2015, San Francisco, CA, USA, July 18-24, 2015, Proceedings, Part II, pages 3-19, 2015.
Yotam M. Y. Feldman, Constantin Enea, Adam Morrison, Noam Rinetzky, and Sharon Shoham
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Redundancy in Distributed Proofs
Distributed proofs are mechanisms enabling the nodes of a network to collectively and efficiently check the correctness of Boolean predicates on the structure of the network (e.g. having a specific diameter), or on data structures distributed over the nodes (e.g. a spanning tree). We consider well known mechanisms consisting of two components: a prover that assigns a certificate to each node, and a distributed algorithm called verifier that is in charge of verifying the distributed proof formed by the collection of all certificates. We show that many network predicates have distributed proofs offering a high level of redundancy, explicitly or implicitly. We use this remarkable property of distributed proofs to establish perfect tradeoffs between the size of the certificate stored at every node, and the number of rounds of the verification protocol.
Distributed verification
Distributed graph algorithms
Proof-labeling schemes
Space-time tradeoffs
Non-determinism
Networks~Error detection and error correction
Theory of computation~Distributed computing models
Computer systems organization~Redundancy
24:1-24:18
Regular Paper
Research supported by the French-Israeli Laboratory on Foundations of Computer Science (FILOFOCS). The first four authors supported by the ANR project DESCARTES. The first two authors receive additional support from INRIA project GANG. Third author supported by the Ulla Tuominen Foundation. Fourth author supported by the Fondation Sciences Mathématiques de Paris (FSMP).
https://arxiv.org/abs/1803.03031
Laurent
Feuilloley
Laurent Feuilloley
IRIF, CNRS and University Paris Diderot, France
Pierre
Fraigniaud
Pierre Fraigniaud
IRIF, CNRS and University Paris Diderot, France
Juho
Hirvonen
Juho Hirvonen
University of Freiburg, Germany
Ami
Paz
Ami Paz
IRIF, CNRS and University Paris Diderot, France
Mor
Perry
Mor Perry
School of Electrical Engineering, Tel-Aviv University, Israel
10.4230/LIPIcs.DISC.2018.24
Amir Abboud, Keren Censor-Hillel, and Seri Khoury. Near-linear lower bounds for distributed distance computations, even in sparse networks. In 30th Int. Symposium on Distributed Computing (DISC), pages 29-42, 2016. Full version at arXiv:1605.05109.
Yehuda Afek and Shlomi Dolev. Local stabilizer. J. Parallel Distrib. Comput., 62(5):745-765, 2002. URL: http://dx.doi.org/10.1006/jpdc.2001.1823.
http://dx.doi.org/10.1006/jpdc.2001.1823
Yehuda Afek, Shay Kutten, and Moti Yung. The local detection paradigm and its applications to self-stabilization. Theoretical Computer Science, 186(1):199-229, 1997. URL: http://dx.doi.org/10.1016/S0304-3975(96)00286-1.
http://dx.doi.org/10.1016/S0304-3975(96)00286-1
Heger Arfaoui, Pierre Fraigniaud, David Ilcinkas, and Fabien Mathieu. Distributedly testing cycle-freeness. In 40th Int. Workshop on Graph-Theoretic Concepts in Computer Science (WG), volume 8747 of LNCS, pages 15-28. Springer, 2014.
Heger Arfaoui, Pierre Fraigniaud, and Andrzej Pelc. Local decision and verification with bounded-size outputs. In 15th Symp. on Stabilization, Safety, and Security of Distributed Systems (SSS), volume 8255 of LNCS, pages 133-147. Springer, 2013.
Baruch Awerbuch, Boaz Patt-Shamir, and George Varghese. Self-stabilization by local checking and correction. In 32nd Symposium on Foundations of Computer Science (FOCS), pages 268-277. IEEE, 1991.
Alkida Balliu, Gianlorenzo D'Angelo, Pierre Fraigniaud, and Dennis Olivetti. What can be verified locally? In 34th Symposium on Theoretical Aspects of Computer Science (STACS), volume 66 of LIPIcs, pages 8:1-8:13, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.STACS.2017.8.
http://dx.doi.org/10.4230/LIPIcs.STACS.2017.8
Evangelos Bampas and David Ilcinkas. On mobile agent verifiable problems. In 12th Latin American Symposium on Theoretical Informatics (LATIN), LNCS 9644, pages 123-137. Springer, 2016. URL: http://dx.doi.org/10.1007/978-3-662-49529-2_10.
http://dx.doi.org/10.1007/978-3-662-49529-2_10
Mor Baruch, Pierre Fraigniaud, and Boaz Patt-Shamir. Randomized proof-labeling schemes. In 24th Symposium on Principles of Distributed Computing (PODC), pages 315-324. ACM, 2015. URL: http://dx.doi.org/10.1145/2767386.2767421.
http://dx.doi.org/10.1145/2767386.2767421
Joffroy Beauquier, Sylvie Delaët, Shlomi Dolev, and Sébastien Tixeuil. Transient fault detectors. Distributed Computing, 20(1):39-51, 2007. URL: http://dx.doi.org/10.1007/s00446-007-0029-x.
http://dx.doi.org/10.1007/s00446-007-0029-x
Lélia Blin and Pierre Fraigniaud. Space-optimal time-efficient silent self-stabilizing constructions of constrained spanning trees. In 35th Int. Conference on Distributed Computing Systems (ICDCS), pages 589-598. IEEE, 2015. URL: http://dx.doi.org/10.1109/ICDCS.2015.66.
http://dx.doi.org/10.1109/ICDCS.2015.66
Lélia Blin, Pierre Fraigniaud, and Boaz Patt-Shamir. On proof-labeling schemes versus silent self-stabilizing algorithms. In 16th Int. Symp. on Stabilization, Safety, and Security of Distributed Systems (SSS), LNCS, pages 18-32. Springer, 2014.
Keren Censor-Hillel, Ami Paz, and Mor Perry. Approximate proof labeling schemes. In 24th Int. Colloquium on Structural Information and Communication Complexity (SIROCCO), 2017.
A. Das Sarma, S. Holzer, L. Kor, A. Korman, D. Nanongkai, G. Pandurangan, D. Peleg, and R. Wattenhofer. Distributed verification and hardness of distributed approximation. SIAM J. Comput., 41(5):1235-1265, 2012.
Laurent Feuilloley and Pierre Fraigniaud. Survey of distributed decision. Bulletin of the EATCS, 119, 2016. URL: http://bulletin.eatcs.org/index.php/beatcs/article/view/411/391.
http://bulletin.eatcs.org/index.php/beatcs/article/view/411/391
Laurent Feuilloley and Pierre Fraigniaud. Error-sensitive proof-labeling schemes. In 31st International Symposium on Distributed Computing (DISC), pages 16:1-16:15, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.DISC.2017.16.
http://dx.doi.org/10.4230/LIPIcs.DISC.2017.16
Laurent Feuilloley, Pierre Fraigniaud, and Juho Hirvonen. A Hierarchy of Local Decision. In 43rd Int. Colloquium on Automata, Languages, and Programming (ICALP), LIPIcs, pages 118:1-118:15, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.118.
http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.118
Klaus-Tycho Foerster, Thomas Luedi, Jochen Seidel, and Roger Wattenhofer. Local checkability, no strings attached: (a)cyclicity, reachability, loop free updates in sdns. Theor. Comput. Sci., 709:48-63, 2018. URL: http://dx.doi.org/10.1016/j.tcs.2016.11.018.
http://dx.doi.org/10.1016/j.tcs.2016.11.018
Pierre Fraigniaud, Amos Korman, and David Peleg. Towards a complexity theory for local distributed computing. J. ACM, 60(5):35, 2013.
Pierre Fraigniaud and Andrzej Pelc. Decidability classes for mobile agents computing. J. Parallel Distrib. Comput., 109:117-128, 2017. URL: http://dx.doi.org/10.1016/j.jpdc.2017.04.003.
http://dx.doi.org/10.1016/j.jpdc.2017.04.003
Pierre Fraigniaud, Sergio Rajsbaum, and Corentin Travers. Minimizing the number of opinions for fault-tolerant distributed decision using well-quasi orderings. In 12th Latin American Symposium on Theoretical Informatics (LATIN), pages 497-508. Springer, 2016. URL: http://dx.doi.org/10.1007/978-3-662-49529-2_37.
http://dx.doi.org/10.1007/978-3-662-49529-2_37
Pierre Fraigniaud, Sergio Rajsbaum, Corentin Travers, Petr Kuznetsov, and Thibault Rieutord. Perfect failure detection with very few bits. In 18th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), LNCS 10083, pages 154-169. Springer, 2016. URL: http://dx.doi.org/10.1007/978-3-319-49259-9_13.
http://dx.doi.org/10.1007/978-3-319-49259-9_13
Silvio Frischknecht, Stephan Holzer, and Roger Wattenhofer. Networks cannot compute their diameter in sublinear time. In 23rd Symposium on Discrete Algorithms (SODA), pages 1150-1162. ACM-SIAM, 2012.
R. G. Gallager, P. A. Humblet, and P. M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Transactions on Programming Languages and Systems (TOPLAS), 5(1):66-77, 1983. URL: http://dx.doi.org/10.1145/357195.357200.
http://dx.doi.org/10.1145/357195.357200
Mika Göös and Jukka Suomela. Locally checkable proofs in distributed computing. Theory of Computing, 12(1):1-33, 2016. URL: http://dx.doi.org/10.4086/toc.2016.v012a019.
http://dx.doi.org/10.4086/toc.2016.v012a019
Gene Itkis and Leonid A. Levin. Fast and lean self-stabilizing asynchronous protocols. In 35th Symposium on Foundations of Computer Science (FOCS), pages 226-239. IEEE, 1994. URL: http://dx.doi.org/10.1109/SFCS.1994.365691.
http://dx.doi.org/10.1109/SFCS.1994.365691
Gillat Kol, Rotem Oshman, and Raghuvansh R. Saxena. Interactive distributed proofs. In 37th ACM Symposium on Principles of Distributed Computing (PODC 2018), to appear.
Janne H. Korhonen and Jukka Suomela. Brief announcement: Towards a complexity theory for the congested clique. In 31st International Symposium on Distributed Computing (DISC), pages 55:1-55:3, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.DISC.2017.55.
http://dx.doi.org/10.4230/LIPIcs.DISC.2017.55
Amos Korman and Shay Kutten. Distributed verification of minimum spanning trees. Distributed Computing, 20:253-266, 2007.
Amos Korman, Shay Kutten, and Toshimitsu Masuzawa. Fast and compact self-stabilizing verification, computation, and fault detection of an MST. Distributed Computing, 28(4):253-295, 2015. URL: http://dx.doi.org/10.1007/s00446-015-0242-y.
http://dx.doi.org/10.1007/s00446-015-0242-y
Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. Distributed Computing, 22(4):215-233, 2010. URL: http://dx.doi.org/10.1007/s00446-010-0095-3.
http://dx.doi.org/10.1007/s00446-010-0095-3
Eyal Kushilevitz and Noam Nisan. Communication complexity. Cambridge University Press, New York, 1997.
Rafail Ostrovsky, Mor Perry, and Will Rosenbaum. Space-time tradeoffs for distributed verification. In 24th International Colloquium on Structural Information and Communication Complexity (SIROCCO), pages 53-70, 2017. URL: http://dx.doi.org/10.1007/978-3-319-72050-0_4.
http://dx.doi.org/10.1007/978-3-319-72050-0_4
Boaz Patt-Shamir and Mor Perry. Proof-labeling schemes: Broadcast, unicast and in between. In 19th Int. Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), LNCS 10616, pages 1-17. Springer, 2017. URL: http://dx.doi.org/10.1007/978-3-319-69084-1_1.
http://dx.doi.org/10.1007/978-3-319-69084-1_1
David Peleg. Distributed Computing: A Locality-Sensitive Approach. Discrete Mathematics and Applications. SIAM, Philadelphia, 2000.
David Peleg and Vitaly Rubinovich. A near-tight lower bound on the time complexity of distributed MST construction. In 40th Symp. on Foundations of Computer Science (FOCS), pages 253-261. IEEE, 1999. URL: http://dx.doi.org/10.1109/SFFCS.1999.814597.
http://dx.doi.org/10.1109/SFFCS.1999.814597
Laurent Feuilloley, Pierre Fraigniaud, Juho Hirvonen, Ami Paz, and Mor Perry
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Local Verification of Global Proofs
In this work we study the cost of local and global proofs on distributed verification. In this setting the nodes of a distributed system are provided with a nondeterministic proof for the correctness of the state of the system, and the nodes need to verify this proof by looking at only their local neighborhood in the system.
Previous works have studied the model where each node is given its own, possibly unique, part of the proof as input. The cost of a proof is the maximum size of an individual label. We compare this model to a model where each node has access to the same global proof, and the cost is the size of this global proof.
It is easy to see that a global proof can always include all of the local proofs, and every local proof can be a copy of the global proof. We show that there exists properties that exhibit these relative proof sizes, and also properties that are somewhere in between. In addition, we introduce a new lower bound technique and use it to prove a tight lower bound on the complexity of reversing distributed decision and establish a link between communication complexity and distributed proof complexity.
Proof-labeling schemes
distributed verification
non-determinism
local proofs
Theory of computation~Distributed computing models
Theory of computation~Proof complexity
25:1-25:17
Regular Paper
Laurent
Feuilloley
Laurent Feuilloley
University Paris Diderot, France
https://orcid.org/0000-0002-3994-0898
Additional support from ANR project DESCARTES and INRIA project GANG.
Juho
Hirvonen
Juho Hirvonen
University of Freiburg, Germany
Supported by Ulla Tuominen Foundation.
10.4230/LIPIcs.DISC.2018.25
Lazslo Babai, Peter Frankl, and Janos Simon. Complexity classes in communication complexity theory. In Proc. 27th Annual Symposium on Foundations of Computer Science (FOCS 1986), pages 337-347, 1986. URL: http://dx.doi.org/10.1109/SFCS.1986.15.
http://dx.doi.org/10.1109/SFCS.1986.15
Jørgen Bang-Jensen and Gregory Gutin. Digraphs - theory, algorithms and applications. Springer, 2002.
Keren Censor-Hillel, Ami Paz, and Mor Perry. Approximate proof-labeling schemes. In Structural Information and Communication Complexity - 24th International Colloquium, SIROCCO 2017, Porquerolles, France, June 19-22, 2017, Revised Selected Papers, pages 71-89, 2017. URL: http://dx.doi.org/10.1007/978-3-319-72050-0_5.
http://dx.doi.org/10.1007/978-3-319-72050-0_5
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, 3rd Edition. MIT Press, 2009. URL: http://mitpress.mit.edu/books/introduction-algorithms.
http://mitpress.mit.edu/books/introduction-algorithms
Laurent Feuilloley and Pierre Fraigniaud. Survey of distributed decision. Bulletin of the EATCS, 119, 2016. URL: http://bulletin.eatcs.org/index.php/beatcs/article/view/411/391.
http://bulletin.eatcs.org/index.php/beatcs/article/view/411/391
Laurent Feuilloley and Pierre Fraigniaud. Error-sensitive proof-labeling schemes. In 31st International Symposium on Distributed Computing, DISC 2017, October 16-20, 2017, Vienna, Austria, pages 16:1-16:15, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.DISC.2017.16.
http://dx.doi.org/10.4230/LIPIcs.DISC.2017.16
Laurent Feuilloley, Pierre Fraigniaud, and Juho Hirvonen. A Hierarchy of Local Decision. In Proc. 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), volume 55 of Leibniz International Proceedings in Informatics (LIPIcs), pages 118:1-118:15, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.118.
http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.118
Pierre Fraigniaud, Amos Korman, and David Peleg. Local distributed decision. In IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, Palm Springs, CA, USA, October 22-25, 2011, pages 708-717, 2011. URL: http://dx.doi.org/10.1109/FOCS.2011.17.
http://dx.doi.org/10.1109/FOCS.2011.17
Pierre Fraigniaud, Amos Korman, and David Peleg. Towards a complexity theory for local distributed computing. J. ACM, 60(5):35, 2013. URL: http://dx.doi.org/10.1145/2499228.
http://dx.doi.org/10.1145/2499228
Mika Göös, Toniann Pitassi, and Thomas Watson. The landscape of communication complexity classes. In 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy, pages 86:1-86:15, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.86.
http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.86
Mika Göös and Jukka Suomela. Locally checkable proofs in distributed computing. Theory of Computing, 12(1):1-33, 2016. URL: http://dx.doi.org/10.4086/toc.2016.v012a019.
http://dx.doi.org/10.4086/toc.2016.v012a019
Tom Gur and Ron D. Rothblum. Non-interactive proofs of proximity. In Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science, ITCS 2015, Rehovot, Israel, January 11-13, 2015, pages 133-142, 2015. URL: http://dx.doi.org/10.1145/2688073.2688079.
http://dx.doi.org/10.1145/2688073.2688079
Amos Korman and Shay Kutten. Distributed verification of minimum spanning trees. Distributed Computing, 20(4):253-266, 2007. URL: http://dx.doi.org/10.1007/s00446-007-0025-1.
http://dx.doi.org/10.1007/s00446-007-0025-1
Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. In Proceedings of the Twenty-Fourth Annual ACM Symposium on Principles of Distributed Computing, PODC 2005, Las Vegas, NV, USA, July 17-20, 2005, pages 9-18, 2005. URL: http://dx.doi.org/10.1145/1073814.1073817.
http://dx.doi.org/10.1145/1073814.1073817
Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. Distributed Computing, 22(4):215-233, 2010. URL: http://dx.doi.org/10.1007/s00446-010-0095-3.
http://dx.doi.org/10.1007/s00446-010-0095-3
Elias Koutsoupias and Christos H. Papadimitriou. Worst-case equilibria. Computer Science Review, 3(2):65-69, 2009. URL: http://dx.doi.org/10.1016/j.cosrev.2009.04.003.
http://dx.doi.org/10.1016/j.cosrev.2009.04.003
Fabian Kuhn. The price of locality: exploring the complexity of distributed coordination primitives. PhD thesis, ETH Zurich, 2005. URL: http://d-nb.info/977273725.
http://d-nb.info/977273725
Eyal Kushilevitz and Noam Nisan. Communication complexity. Cambridge University Press, 1997.
László Lovász and Katalin Vesztergombi. Non-deterministic graph property testing. Combinatorics, Probability & Computing, 22(5):749-762, 2013. URL: http://dx.doi.org/10.1017/S0963548313000205.
http://dx.doi.org/10.1017/S0963548313000205
Rafail Ostrovsky, Mor Perry, and Will Rosenbaum. Space-time tradeoffs for distributed verification. In Structural Information and Communication Complexity - 24th International Colloquium, SIROCCO 2017, Porquerolles, France, June 19-22, 2017, Revised Selected Papers, pages 53-70, 2017. URL: http://dx.doi.org/10.1007/978-3-319-72050-0_4.
http://dx.doi.org/10.1007/978-3-319-72050-0_4
Christos H. Papadimitriou. Algorithms, games, and the internet. In Proceedings on 33rd Annual ACM Symposium on Theory of Computing, July 6-8, 2001, Heraklion, Crete, Greece, pages 749-753, 2001. URL: http://dx.doi.org/10.1145/380752.380883.
http://dx.doi.org/10.1145/380752.380883
Boaz Patt-Shamir and Mor Perry. Proof-labeling schemes: Broadcast, unicast and in between. In Stabilization, Safety, and Security of Distributed Systems - 19th International Symposium, SSS 2017, Boston, MA, USA, November 5-8, 2017, Proceedings, pages 1-17, 2017. URL: http://dx.doi.org/10.1007/978-3-319-69084-1_1.
http://dx.doi.org/10.1007/978-3-319-69084-1_1
Laurent Feuilloley and Juho Hirvonen
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
A Simple Parallel and Distributed Sampling Technique: Local Glauber Dynamics
Sampling constitutes an important tool in a variety of areas: from machine learning and combinatorial optimization to computational physics and biology. A central class of sampling algorithms is the Markov Chain Monte Carlo method, based on the construction of a Markov chain with the desired sampling distribution as its stationary distribution. Many of the traditional Markov chains, such as the Glauber dynamics, do not scale well with increasing dimension. To address this shortcoming, we propose a simple local update rule based on the Glauber dynamics that leads to efficient parallel and distributed algorithms for sampling from Gibbs distributions.
Concretely, we present a Markov chain that mixes in O(log n) rounds when Dobrushin's condition for the Gibbs distribution is satisfied. This improves over the LubyGlauber algorithm by Feng, Sun, and Yin [PODC'17], which needs O(Delta log n) rounds, and their LocalMetropolis algorithm, which converges in O(log n) rounds but requires a considerably stronger mixing condition. Here, n denotes the number of nodes in the graphical model inducing the Gibbs distribution, and Delta its maximum degree. In particular, our method can sample a uniform proper coloring with alpha Delta colors in O(log n) rounds for any alpha >2, which almost matches the threshold of the sequential Glauber dynamics and improves on the alpha>2 + sqrt{2} threshold of Feng et al.
Distributed Graph Algorithms
Parallel Algorithms
Local Algorithms
Locality
Sampling
Glauber Dynamics
Coloring
Theory of computation~Distributed algorithms
26:1-26:11
Regular Paper
https://arxiv.org/abs/1802.06676
Manuela
Fischer
Manuela Fischer
ETH Zurich, Switzerland
Mohsen
Ghaffari
Mohsen Ghaffari
ETH Zurich, Switzerland
10.4230/LIPIcs.DISC.2018.26
Christophe Andrieu, Nando De Freitas, Arnaud Doucet, and Michael I. Jordan. An Introduction to MCMC for Machine Learning. Machine Learning, 50(1-2):5-43, 2003.
Russ Bubley and Martin Dyer. Path Coupling: A Technique for Proving Rapid Mixing in Markov Chains. In the Proceedings of the Symposium on Foundations of Computer Science (FOCS), pages 223-231, 1997.
Sitan Chen and Ankur Moitra. Linear Programming Bounds for Randomly Sampling Colorings. arXiv preprint arXiv:1804.03156, 2018.
Michelle Delcourt, Guillem Perarnau, and Luke Postle. Rapid Mixing of Glauber Dynamics for Colorings Below Vigoda’s 11/6 Threshold. arXiv preprint arXiv:1804.04025, 2018.
Roland L. Dobruschin. The Description of a Random Field by Means of Conditional Probabilities and Conditions of its Regularity. Theory of Probability &Its Applications, 13(2):197-224, 1968.
Weiming Feng, Thomas P. Hayes, and Yitong Yin. Distributed Symmetry Breaking in Sampling (Optimal Distributed Randomly Coloring with Fewer Colors). arXiv preprint arXiv:1802.06953, 2018.
Weiming Feng, Yuxin Sun, and Yitong Yin. What Can Be Sampled Locally? In Proceedings of the International Symposium on Principles of Distributed Computing (PODC), pages 121-130, 2017.
Alan Frieze and Eric Vigoda. A Survey on the Use of Markov Chains to Randomly Sample Colourings. Oxford Lecture Series in Mathematics and its Applications, 34:53, 2007.
Joseph Gonzalez, Yucheng Low, Arthur Gretton, and Carlos Guestrin. Parallel Gibbs Sampling: From Colored Fields to Thin Junction Trees. In the Proceedings of the International Conference on Artificial Intelligence and Statistics, pages 324-332, 2011.
Heng Guo, Mark Jerrum, and Jingcheng Liu. Uniform Sampling Through the Lovász Local Lemma. Proceedings of the Symposium on Theory of Computing (STOC), pages 342-355, 2017.
J. M. Hammersley and P. Clifford. Markov Fields on Finite Graphs and Lattices. Unpublished, available at http://www.statslab.cam.ac.uk/~grg/books/hammfest/hamm-cliff.pdf, 1971.
http://www.statslab.cam.ac.uk/~grg/books/hammfest/hamm-cliff.pdf
Mark Jerrum. A Very Simple Algorithm for Estimating the Number of k-Colorings of a Low-Degree Graph. Random Structures &Algorithms, 7(2):157-165, 1995.
Mark R. Jerrum, Leslie G. Valiant, and Vijay V. Vazirani. Random Generation of Combinatorial Structures from a Uniform Distribution. Theoretical Computer Science, 43:169-188, 1986.
Nathan Linial. Distributive Graph Algorithms - Global Solutions From Local Data. In the Proceedings of the Symposium on Foundations of Computer Science (FOCS), pages 331-335. IEEE, 1987.
Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. Equation of State Calculations by Fast Computing Machines. The Journal of Chemical Physics, 21(6):1087-1092, 1953.
Surendra Nahar, Sartaj Sahni, and Eugene Shragowitz. Simulated Annealing and Combinatorial Optimization. In Proceedings of the Design Automation Conference, pages 293-299. IEEE Press, 1986.
Moni Naor and Larry Stockmeyer. What Can Be Computed Locally? SIAM Journal on Computing, 24(6):1259-1277, 1995.
David Newman, Padhraic Smyth, Max Welling, and Arthur U. Asuncion. Distributed Inference for Latent Dirichlet Allocation. In Advances in Neural Information Processing Systems, pages 1081-1088, 2008.
Jesús Salas and Alan D. Sokal. Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem. Journal of Statistical Physics, 86(3-4):551-579, 1997.
Eric Vigoda. Improved Bounds for Sampling Colorings. Journal of Mathematical Physics, 41(3):1555-1569, 2000.
Feng Yan, Ningyi Xu, and Yuan Qi. Parallel Inference for Latent Dirichlet Allocation on Graphics Processing Units. In Advances in Neural Information Processing Systems, pages 2134-2142, 2009.
Manuela Fischer and Mohsen Ghaffari
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Fast Multidimensional Asymptotic and Approximate Consensus
We study the problems of asymptotic and approximate consensus in which agents have to get their values arbitrarily close to each others' inside the convex hull of initial values, either without or with an explicit decision by the agents. In particular, we are concerned with the case of multidimensional data, i.e., the agents' values are d-dimensional vectors. We introduce two new algorithms for dynamic networks, subsuming classical failure models like asynchronous message passing systems with Byzantine agents. The algorithms are the first to have a contraction rate and time complexity independent of the dimension d. In particular, we improve the time complexity from the previously fastest approximate consensus algorithm in asynchronous message passing systems with Byzantine faults by Mendes et al. [Distrib. Comput. 28] from Omega(d log (d Delta)/epsilon) to O(log Delta/epsilon), where Delta is the initial and epsilon is the terminal diameter of the set of vectors of correct agents.
asymptotic consensus
approximate consensus
multidimensional data
dynamic networks
Byzantine processes
Theory of computation~Distributed algorithms
27:1-27:16
Regular Paper
This research was partially supported by the CNRS project PEPS DEMO and the Institut Farman.
Matthias
Függer
Matthias Függer
CNRS, LSV, ENS Paris-Saclay, Université Paris-Saclay, and Inria, France
Thomas
Nowak
Thomas Nowak
Université Paris-Sud, France
10.4230/LIPIcs.DISC.2018.27
Ittai Abraham, Yonatan Amit, and Danny Dolev. Optimal resilience asynchronous approximate agreement. In Teruo Higashino, editor, 8th International Conference on Principles of Distributed Systems (OPODIS 2004), volume 3544 of Lecture Notes in Computer Science, pages 229-239. Springer, Heidelberg, 2005.
David Angeli and Pierre-Alexandre Bliman. Stability of leaderless discrete-time multi-agent systems. MCSS, 18(4):293-322, 2006.
Zohir Bouzid, Maria Gradinariu Potop-Butucaru, and Sébastien Tixeuil. Optimal Byzantine-resilient convergence in uni-dimensional robot networks. Theoretical Computer Science, 411(34-36):3154-3168, 2010.
Stephen Boyd and Lieven Vandenberghe. Convex optimization. Cambridge University Press, 2004.
Ming Cao, A. Stephen Morse, and Brian D. O. Anderson. Reaching a consensus in a dynamically changing environment: convergence rates, measurement delays, and asynchronous events. SIAM J. Control Optim., 47(2):601-623, 2008.
Bernadette Charron-Bost, Matthias Függer, and Thomas Nowak. Approximate consensus in highly dynamic networks: The role of averaging algorithms. In Proceedings of the 42nd International Colloquium on Automata, Languages, and Programming, ICALP15, pages 528-539, 2015.
Bernadette Charron-Bost, Matthias Függer, and Thomas Nowak. Fast, robust, quantizable approximate consensus. In Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming, ICALP16, pages 137:1-137:14, 2016.
Bernadette Charron-Bost, Matthias Függer, and Thomas Nowak. Multidimensional asymptotic consensus in dynamic networks. CoRR, abs/1611.02496, 2016. URL: http://arxiv.org/abs/1611.02496.
http://arxiv.org/abs/1611.02496
Bernadette Charron-Bost and André Schiper. The Heard-Of model: computing in distributed systems with benign faults. Distrib. Comput., 22(1):49-71, 2009.
Bernard Chazelle. The total s-energy of a multiagent system. SIAM Journal on Control and Optimization, 49(4):1680-1706, 2011.
Mark Cieliebak, Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Solving the robots gathering problem. In International Colloquium on Automata, Languages, and Programming, pages 1181-1196. Springer, 2003.
Ludwig Danzer, Branko Grünbaum, and Victor Klee. Helly’s theorem and its relatives. In Victor Klee, editor, Convexity, volume 7 of Proceedings of Symposia in Pure Mathematics, pages 101-180. AMS, Providence, 1963.
Danny Dolev, Nancy A. Lynch, Shlomit S. Pinter, Eugene W. Stark, and William E. Weihl. Reaching approximate agreement in the presence of faults. jacm, 33(2):499-516, 1986.
Alan D. Fekete. Asymptotically optimal algorithms for approximate agreement. Distrib. Comput., 4(1):9-29, 1990.
Matthias Függer, Thomas Nowak, and Manfred Schwarz. Tight bounds for asymptotic and approximate consensus. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC '18, pages 325-334, 2018.
Qun Li and Daniela Rus. Global clock synchronization in sensor networks. IEEE Transactions on Computers, 55(2):214-226, 2006.
Nancy A. Lynch. Distributed Algorithms. Morgan Kaufmann, San Francisco, CA, 1996.
Hammurabi Mendes, Maurice Herlihy, Nitin Vaidya, and Vijay K. Garg. Multidimensional agreement in Byzantine systems. Distributed Computing, 28:423-441, 2015.
Luc Moreau. Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control, 50(2):169-182, 2005.
Reza Olfati-Saber and Richard M Murray. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on automatic control, 49(9):1520-1533, 2004.
Luis A. Rademacher. Approximating the centroid is hard. In Proceedings of the Twenty-third Annual Symposium on Computational Geometry, pages 302-305. ACM, 2007.
Nicola Santoro and Peter Widmayer. Time is not a healer. In B. Monien and R. Cori, editors, 6th Symposium on Theoretical Aspects of Computer Science, volume 349 of LNCS, pages 304-313. Springer, Heidelberg, 1989.
Fred B Schneider. Understanding protocols for Byzantine clock synchronization. Technical report, Cornell University, 1987.
Jennifer Lundelius Welch and Nancy Lynch. A new fault-tolerant algorithm for clock synchronization. Information and computation, 77(1):1-36, 1988.
Matthias Függer and Thomas Nowak
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Local Queuing Under Contention
We study stability of local packet scheduling policies in a distributed system of n nodes. The local policies at nodes may only access their local queues, and have no other feedback from the underlying distributed system. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate rho and burstiness b. In this work, we assume that the underlying distributed system is a shared channel, in which in order to get rid of a packet from the queue, a node needs to schedule it for transmission on the channel and no other packet is scheduled for transmission at the same time. We show that there is a local adaptive scheduling policy with relatively small memory, which is universally stable on a shared channel, that is, it has bounded queues for any rho<1 and b >= 0. On the other hand, without memory the maximal stable injection rate is O(1/log n). We show a local memoryless (non-adaptive) scheduling policy based on novel idea of ultra strong selectors which is stable for slightly smaller injection c/log^2 n, for some constant c>0.
Distributed algorithms
local queuing
shared channel
multiple-access channel
adversarial packet arrivals
stability
deterministic algorithms
Theory of computation~Distributed algorithms
28:1-28:18
Regular Paper
Supported by Polish National Science Center grant 2017/25/B/ST6/02010.
Pawel
Garncarek
Pawel Garncarek
Institute of Computer Science, University of Wroclaw, Poland
Tomasz
Jurdzinski
Tomasz Jurdzinski
Institute of Computer Science, University of Wroclaw, Poland
Dariusz R.
Kowalski
Dariusz R. Kowalski
Computer Science Department, University of Liverpool, Liverpool, UK
10.4230/LIPIcs.DISC.2018.28
Norman M. Abramson. Development of the ALOHANET. IEEE Transactions on Information Theory, 31(2):119-123, 1985.
Noga Alon, Amotz Bar-Noy, Nathan Linial, and David Peleg. A lower bound for radio broadcast. Journal of Computer and System Sciences, 43(2):290-298, 1991. URL: http://dx.doi.org/10.1016/0022-0000(91)90015-W.
http://dx.doi.org/10.1016/0022-0000(91)90015-W
L. Anantharamu, Bogdan S. Chlebus, and Mariusz A. Rokicki. Adversarial multiple access channel with individual injection rates. In Proceedings of the 13th International Conference on Principles of Distributed Systems (OPODIS), LNCS 5923, pages 174-188. Springer-Verlag, 2009.
Lakshmi Anantharamu, Bogdan S. Chlebus, Dariusz R. Kowalski, and Mariusz A. Rokicki. Deterministic broadcast on multiple access channels. In Proceedings of the 29th IEEE International Conference on Computer Communications (INFOCOM), pages 1-5, 2010.
Matthew Andrews, Baruch Awerbuch, Antonio Fernández, Frank Thomson Leighton, Zhiyong Liu, and Jon M. Kleinberg. Universal-stability results and performance bounds for greedy contention-resolution protocols. Journal of the ACM, 48(1):39-69, 2001.
Michael A. Bender, Martin Farach-Colton, Simai He, Bradley C. Kuszmaul, and Charles E. Leiserson. Adversarial contention resolution for simple channels. In Proceedings of the 17th Annual ACM Symposium on Parallel Algorithms (SPAA), pages 325-332, 2005.
Marcin Bieńkowski, Marek Klonowski, Mirosław Korzeniowski, and Dariusz R. Kowalski. Dynamic sharing of a multiple access channel. In Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science (STACS), pages 83-94, 2010.
Allan Borodin, Jon M. Kleinberg, Prabhakar Raghavan, Madhu Sudan, and David P. Williamson. Adversarial queuing theory. Journal of the ACM, 48(1):13-38, 2001.
Bogdan S. Chlebus, Dariusz R. Kowalski, and Mariusz A. Rokicki. Maximum throughput of multiple access channels in adversarial environments. Distributed Computing, 22(2):93-116, 2009.
Bogdan S. Chlebus, Dariusz R. Kowalski, and Mariusz A. Rokicki. Adversarial queuing on the multiple access channel. ACM Transactions on Algorithms, 8(1):5:1-5:31, 2012.
Jurek Czyżowicz, Leszek Gąsieniec, Dariusz R. Kowalski, and Andrzej Pelc. Consensus and mutual exclusion in a multiple access channel. In Proceedings of the 23rd International Symposium on Distributed Computing (DISC), LNCS 5805, pages 512-526. Springer-Verlag, 2009.
Robert G. Gallager. A perspective on multiaccess channels. IEEE Transactions on Information Theory, 31(2):124-142, 1985.
Leszek Gąsieniec, Andrzej Pelc, and David Peleg. The wakeup problem in synchronous broadcast systems. SIAM Journal on Discrete Mathematics, 14(2):207-222, 2001.
Leslie Ann Goldberg, Mark Jerrum, Sampath Kannan, and Mike Paterson. A bound on the capacity of backoff and acknowledgment-based protocols. SIAM Journal on Computing, 33(2):313-331, 2004.
Leslie Ann Goldberg, Philip D. MacKenzie, Mike Paterson, and Aravind Srinivasan. Contention resolution with constant expected delay. Journal of the ACM, 47(6):1048-1096, 2000.
Albert G. Greenberg and Shmuel Winograd. A lower bound on the time needed in the worst case to resolve conflicts deterministically in multiple access channels. Journal of the ACM, 32(3):589-596, 1985.
J. Håstad, F. T. Leighton, and B. Rogoff. Analysis of backoff protocols for multiple access channels. SIAM Journal on Computing, 25(4):740-774, 1996.
Tomasz Jurdziński, Miroslaw Kutyłowski, and Jan Zatopiański. Efficient algorithms for leader election in radio networks. In Proceedings of the 21st ACM Symposium on Principles of Distributed Computing (PODC), pages 51-57, 2002.
Tomasz Jurdziński and Grzegorz Stachowiak. Probabilistic algorithms for the wakeup problem in single-hop radio networks. In Proceedings of the 13th International Symposium on Algorithms and Computation (ISAAC), LNCS 2518, pages 535-549. Springer-Verlag, 2002.
János Komlós and Albert G. Greenberg. An asymptotically fast nonadaptive algorithm for conflict resolution in multiple-access channels. IEEE Transactions on Information Theory, 31(2):302-306, 1985.
Dariusz R. Kowalski. On selection problem in radio networks. In Proceedings of the 24th ACM Symposium on Principles of Distributed Computing (PODC), pages 158-166, 2005.
Eyal Kushilevitz and Yishay Mansour. An Ω(D log (N/D)) lower bound for broadcast in radio networks. SIAM Journal on Computing, 27(3):702-712, 1998.
Robert M. Metcalfe and David R. Boggs. Ethernet: Distributed packet switching for local computer networks. Communications of the ACM, 19(7):395-404, 1976.
Prabhakar Raghavan and Eli Upfal. Stochastic contention resolution with short delays. SIAM Journal on Computing, 28(2):709-719, 1998.
Dan E. Willard. Log-logarithmic selection resolution protocols in a multiple access channel. SIAM Journal on Computing, 15(2):468-477, 1986.
Paweł Garncarek, Tomasz Jurdziński, and Dariusz R. Kowalski
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Derandomizing Distributed Algorithms with Small Messages: Spanners and Dominating Set
This paper presents improved deterministic distributed algorithms, with O(log n)-bit messages, for some basic graph problems. The common ingredient in our results is a deterministic distributed algorithm for computing a certain hitting set, which can replace the random part of a number of standard randomized distributed algorithms. This deterministic hitting set algorithm itself is derived using a simple method of conditional expectations. As one main end-result of this derandomized hitting set, we get a deterministic distributed algorithm with round complexity 2^O(sqrt{log n * log log n}) for computing a (2k-1)-spanner of size O~(n^{1+1/k}). This improves considerably on a recent algorithm of Grossman and Parter [DISC'17] which needs O(n^{1/2-1/k} * 2^k) rounds. We also get a 2^O(sqrt{log n * log log n})-round deterministic distributed algorithm for computing an O(log^2 n)-approximation of minimum dominating set; all prior algorithms for this problem were either randomized or required large messages.
Distributed Algorithms
Derandomization
Spanners
Dominating Set
Theory of computation~Distributed algorithms
29:1-29:17
Regular Paper
A full version of the paper is available at [M. Ghaffari and F. Kuhn, 2018], http://tr.informatik.uni-freiburg.de/reports/report285/report00285.pdf.
Mohsen
Ghaffari
Mohsen Ghaffari
ETH Zurich, Switzerland
Fabian
Kuhn
Fabian Kuhn
University of Freiburg, Germany
10.4230/LIPIcs.DISC.2018.29
Noga Alon and Joel H Spencer. The probabilistic method. John Wiley &Sons, 2004.
Matti Åstrand and Jukka Suomela. Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks. In Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures, pages 294-302. ACM, 2010.
B. Awerbuch, AV Goldberg, M. Luby, and S. Plotkin. Network decomposition and locality in distributed computation. In FOCS, pages 364-369, 1989.
Baruch Awerbuch. Complexity of network synchronization. Journal of the ACM (JACM), 32(4):804-823, 1985.
Baruch Awerbuch and David Peleg. Sparse partitions. In Proc. IEEE Symp. on Foundations of Computer Science (FOCS), pages 503-513, 1990.
Leonid Barenboim and Michael Elkin. Distributed graph coloring: Fundamentals and recent developments. Synthesis Lectures on Distributed Computing Theory, 4(1):1-171, 2013.
Leonid Barenboim, Michael Elkin, and Cyril Gavoille. A fast network-decomposition algorithm and its applications to constant-time distributed computation. Theoretical Computer Science, 2016.
Surender Baswana and Sandeep Sen. A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs. Random Structures &Algorithms, 30(4):532-563, 2007.
Keren Censor-Hillel, Merav Parter, and Gregory Schwartzman. Derandomizing local distributed algorithms under bandwidth restrictions. In 31 International Symposium on Distributed Computing, 2017.
Bilel Derbel and Cyril Gavoille. Fast deterministic distributed algorithms for sparse spanners. In International Colloquium on Structural Information and Communication Complexity, pages 100-114. Springer, 2006.
Bilel Derbel, Cyril Gavoille, and David Peleg. Deterministic distributed construction of linear stretch spanners in polylogarithmic time. In International Symposium on Distributed Computing, pages 179-192. Springer, 2007.
Bilel Derbel, Cyril Gavoille, David Peleg, and Laurent Viennot. On the locality of distributed sparse spanner construction. In Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing, pages 273-282. ACM, 2008.
Bilel Derbel, Mohamed Mosbah, and Akka Zemmari. Sublinear fully distributed partition with applications. Theory of Computing Systems, 47(2):368-404, 2010.
Paul Erdős. Some problems in graph theory. In STUDIA SIC MATH. HUNGAR. Citeseer, 1966.
M. Ghaffari and F. Kuhn. Derandomizing distributed algorithms with small messages: Spanners and dominating set. Technical Report 285, U. of Freiburg, Dept. of Computer Science, 2018. URL: http://tr.informatik.uni-freiburg.de/reports/report285/report00285.pdf.
http://tr.informatik.uni-freiburg.de/reports/report285/report00285.pdf
Mohsen Ghaffari. An improved distributed algorithm for maximal independent set. In Pro. ACM-SIAM Symp. on Discrete Algorithms (SODA), 2016.
Mohsen Ghaffari, David G Harris, and Fabian Kuhn. On derandomizing local distributed algorithms. arXiv preprint arXiv:1711.02194, 2017.
Ofer Grossman and Merav Parter. Improved deterministic distributed construction of spanners. In 31 International Symposium on Distributed Computing, 2017.
Lujun Jia, Rajmohan Rajaraman, and Torsten Suel. An efficient distributed algorithm for constructing small dominating sets. Distributed Computing, 15(4):193-205, 2002.
Ken-Ichi Kawarabayashi and Gregory Schwartzman. Adapting local sequential algorithms to the distributed setting. arXiv preprint arXiv:1711.10155, 2017.
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. Local computation: Lower and upper bounds. J. ACM, 63(2):17:1-17:44, mar 2016.
Fabian Kuhn and Roger Wattenhofer. Constant-time distributed dominating set approximation. In Proc. ACM Symp. on Principles of Distributed Computing (PODC), pages 25-32, 2003.
Christoph Lenzen and Roger Wattenhofer. Minimum dominating set approximation in graphs of bounded arboricity. In International Symposium on Distributed Computing, pages 510-524. Springer, 2010.
Nathan Linial. Distributive graph algorithms global solutions from local data. In Proc. IEEE Symp. on Foundations of Computer Science (FOCS), pages 331-335. IEEE, 1987.
Michael Luby. Removing randomness in parallel computation without a processor penalty. Journal of Computer and System Sciences, 47(2):250-286, 1993.
Moni Naor and Larry Stockmeyer. What can be computed locally? SIAM Journal on Computing, 24(6):1259-1277, 1995.
Alessandro Panconesi and Aravind Srinivasan. Improved distributed algorithms for coloring and network decomposition problems. In Proc. ACM Symp. on Theory of Computing (STOC), pages 581-592. ACM, 1992.
David Peleg. Distributed Computing: A Locality-sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2000.
David Peleg and Jeffrey D Ullman. An optimal synchronizer for the hypercube. SIAM Journal on computing, 18(4):740-747, 1989.
Jeanette P Schmidt, Alan Siegel, and Aravind Srinivasan. Chernoff-hoeffding bounds for applications with limited independence. SIAM J. on Discrete Math., 8(2):223-250, 1995.
Vijay V Vazirani. Approximation algorithms. Springer Science &Business Media, 2013.
Mohsen Ghaffari and Fabian Kuhn
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Distributed MST and Broadcast with Fewer Messages, and Faster Gossiping
We present a distributed minimum spanning tree algorithm with near-optimal round complexity of O~(D+sqrt{n}) and message complexity O~(min{n^{3/2}, m}). This is the first algorithm with sublinear message complexity and near-optimal round complexity and it improves over the recent algorithms of Elkin [PODC'17] and Pandurangan et al. [STOC'17], which have the same round complexity but message complexity O~(m). Our method also gives the first broadcast algorithm with o(n) time complexity - when that is possible at all, i.e., when D=o(n) - and o(m) messages. Moreover, our method leads to an O~(sqrt{nD})-round GOSSIP algorithm with bounded-size messages. This is the first such algorithm with a sublinear round complexity.
Distributed Algorithms
Minimum Spanning Tree
Round Complexity
Message Complexity
Gossiping
Broadcast
Theory of computation~Distributed algorithms
30:1-30:12
Regular Paper
Mohsen
Ghaffari
Mohsen Ghaffari
ETH Zurich, Switzerland
Fabian
Kuhn
Fabian Kuhn
University of Freiburg, Germany
10.4230/LIPIcs.DISC.2018.30
Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. Graph sketches: sparsification, spanners, and subgraphs. In Proceedings of the 31st symposium on Principles of Database Systems, pages 5-14. ACM, 2012.
Baruch Awerbuch. Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems. In Proc. of the Symp. on Theory of Comp. (STOC), pages 230-240. ACM, 1987.
Baruch Awerbuch, Oded Goldreich, Ronen Vainish, and David Peleg. A trade-off between information and communication in broadcast protocols. Journal of the ACM (JACM), 37(2):238-256, 1990.
Ruben Becker, Andreas Karrenbauer, Sebastian Krinninger, and Christoph Lenzen. Near-optimal approximate shortest paths and transshipment in distributed and streaming models. In LIPIcs-Leibniz International Proceedings in Informatics, volume 91. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017.
Keren Censor-Hillel, Bernhard Haeupler, Jonathan Kelner, and Petar Maymounkov. Global computation in a poorly connected world: fast rumor spreading with no dependence on conductance. In Proceedings of the forty-fourth annual ACM symposium on Theory of computing, pages 961-970. ACM, 2012.
F Chin and HF Ting. An almost linear time and O(nlogn+ e) messages distributed algorithm for minimum-weight spanning trees. In Proc. of the Symp. on Found. of Comp. Sci. (FOCS), pages 257-266. IEEE, 1985.
Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. In Proc. of the Symp. on Theory of Comp. (STOC), pages 363-372, 2011.
Michael Elkin. Unconditional lower bounds on the time-approximation tradeoffs for the distributed minimum spanning tree problem. In Proc. of the Symp. on Theory of Comp. (STOC), pages 331-340, 2004.
Michael Elkin. A simple deterministic distributed mst algorithm, with near-optimal time and message complexities. In Proceedings of the ACM Symposium on Principles of Distributed Computing, pages 157-163. ACM, 2017.
Michalis Faloutsos and Mart Molle. A linear-time optimal-message distributed algorithm for minimum spanning trees. Distributed Computing, 17(2):151-170, 2004.
Eli Gafni. Improvements in the time complexity of two message-optimal election algorithms. In the Proc. of the Int'l Symp. on Princ. of Dist. Comp. (PODC), pages 175-185. ACM, 1985.
Robert G. Gallager, Pierre A. Humblet, and Philip M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Transactions on Programming Languages and systems (TOPLAS), 5(1):66-77, 1983.
J.A. Garay, S. Kutten, and D. Peleg. A sub-linear time distributed algorithm for minimum-weight spanning trees. In Proc. of the Symp. on Found. of Comp. Sci. (FOCS), 1993.
M. Ghaffari and F. Kuhn. Distributed minimum cut approximation. In Proc. of the Int'l Symp. on Dist. Comp. (DISC), pages 1-15, 2013.
Mohsen Ghaffari. Near-optimal distributed approximation of minimum-weight connected dominating set. In International Colloquium on Automata, Languages, and Programming, pages 483-494. Springer, 2014.
Mohsen Ghaffari and Bernhard Haeupler. Distributed algorithms for planar networks ii: Low-congestion shortcuts, mst, and min-cut. In Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, pages 202-219. SIAM, 2016.
Mohsen Ghaffari, Andreas Karrenbauer, Fabian Kuhn, Christoph Lenzen, and Boaz Patt-Shamir. Near-optimal distributed maximum flow. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, pages 81-90. ACM, 2015.
Mohsen Ghaffari, Fabian Kuhn, and Hsin-Hao Su. Distributed mst and routing in almost mixing time. In the Proc. of the Int'l Symp. on Princ. of Dist. Comp. (PODC), pages 131-140. ACM, 2017.
Mohsen Ghaffari and Christoph Lenzen. Near-optimal distributed tree embedding. In International Symposium on Distributed Computing, pages 197-211. Springer, 2014.
Mohsen Ghaffari and Merav Parter. Mst in log-star rounds of congested clique. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, pages 19-28. ACM, 2016.
George Giakkoupis. Tight bounds for rumor spreading in graphs of a given conductance. In Symposium on Theoretical Aspects of Computer Science (STACS2011), volume 9, pages 57-68, 2011.
Bernhard Haeupler. Simple, fast and deterministic gossip and rumor spreading. Journal of the ACM (JACM), 62(6):47, 2015.
James W. Hegeman, Gopal Pandurangan, Sriram V. Pemmaraju, Vivek B. Sardeshmukh, and Michele Scquizzato. Toward optimal bounds in the congested clique: Graph connectivity and MST. In the Proc. of the Int'l Symp. on Princ. of Dist. Comp. (PODC), pages 91-100. ACM, 2015.
Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. In Proceedings of the forty-eighth annual ACM symposium on Theory of Computing, pages 489-498. ACM, 2016.
Tomasz Jurdziński and Krzysztof Nowicki. Mst in o (1) rounds of congested clique. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 2620-2632. SIAM, 2018.
Maleq Khan and Gopal Pandurangan. A fast distributed approximation algorithm for minimum spanning trees. Distributed Computing, 20(6):391-402, 2008.
Valerie King, Shay Kutten, and Mikkel Thorup. Construction and impromptu repair of an mst in a distributed network with o (m) communication. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, pages 71-80. ACM, 2015.
Liah Kor, Amos Korman, and David Peleg. Tight bounds for distributed mst verification. In Symposium on Theoretical Aspects of Computer Science (STACS2011), volume 9, pages 57-68, 2011.
Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. On the complexity of universal leader election. Journal of the ACM (JACM), 62(1):7, 2015.
Shay Kutten and David Peleg. Fast distributed construction of k-dominating sets and applications. In the Proc. of the Int'l Symp. on Princ. of Dist. Comp. (PODC), pages 238-251, 1995.
Christoph Lenzen and Boaz Patt-Shamir. Fast routing table construction using small messages: Extended abstract. In Proc. of the Symp. on Theory of Comp. (STOC), pages 381-390, 2013.
Ali Mashreghi and Valerie King. Time-communication trade-offs for minimum spanning tree construction. In Proceedings of the 18th International Conference on Distributed Computing and Networking, page 8. ACM, 2017.
Danupon Nanongkai. Distributed approximation algorithms for weighted shortest paths. In Proc. of the Symp. on Theory of Comp. (STOC), 2014.
Danupon Nanongkai and Hsin-Hao Su. Almost-tight distributed minimum cut algorithms. In International Symposium on Distributed Computing, pages 439-453. Springer, 2014.
Jaroslav Nešetřil, Eva Milková, and Helena Nešetřilová. Otakar boruvka on minimum spanning tree problem translation of both the 1926 papers, comments, history. Discrete Mathematics, 233(1):3-36, 2001.
Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. A time-and message-optimal distributed algorithm for minimum spanning trees. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages 743-756. ACM, 2017.
David Peleg. Distributed Computing: A Locality-sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2000.
David Peleg and Vitaly Rubinovich. A near-tight lower bound on the time complexity of distributed MST construction. In Proc. of the Symp. on Found. of Comp. Sci. (FOCS), pages 253-, 1999.
Gurdip Singh and Arthur J Bernstein. A highly asynchronous minimum spanning tree protocol. Distributed Computing, 8(3):151-161, 1995.
Mohsen Ghaffari and Fabian Kuhn
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
New Distributed Algorithms in Almost Mixing Time via Transformations from Parallel Algorithms
We show that many classical optimization problems - such as (1 +/- epsilon)-approximate maximum flow, shortest path, and transshipment - can be computed in tau_{mix}(G)* n^o(1) rounds of distributed message passing, where tau_{mix}(G) is the mixing time of the network graph G. This extends the result of Ghaffari et al. [PODC'17], whose main result is a distributed MST algorithm in tau_{mix}(G)* 2^O(sqrt{log n log log n}) rounds in the CONGEST model, to a much wider class of optimization problems. For many practical networks of interest, e.g., peer-to-peer or overlay network structures, the mixing time tau_{mix}(G) is small, e.g., polylogarithmic. On these networks, our algorithms bypass the Omega(sqrt n+D) lower bound of Das Sarma et al. [STOC'11], which applies for worst-case graphs and applies to all of the above optimization problems. For all of the problems except MST, this is the first distributed algorithm which takes o(sqrt n) rounds on a (nontrivial) restricted class of network graphs.
Towards deriving these improved distributed algorithms, our main contribution is a general transformation that simulates any work-efficient PRAM algorithm running in T parallel rounds via a distributed algorithm running in T * tau_{mix}(G)* 2^O(sqrt{log n}) rounds. Work- and time-efficient parallel algorithms for all of the aforementioned problems follow by combining the work of Sherman [FOCS'13, SODA'17] and Peng and Spielman [STOC'14]. Thus, simulating these parallel algorithms using our transformation framework produces the desired distributed algorithms.
The core technical component of our transformation is the algorithmic problem of solving multi-commodity routing - that is, roughly, routing n packets each from a given source to a given destination - in random graphs. For this problem, we obtain a new algorithm running in 2^O(sqrt{log n}) rounds, improving on the 2^O(sqrt{log n log log n}) round algorithm of Ghaffari, Kuhn, and Su [PODC'17]. As a consequence, for the MST problem in particular, we obtain an improved distributed algorithm running in tau_{mix}(G)* 2^O(sqrt{log n}) rounds.
Distributed Graph Algorithms
Mixing Time
Random Graphs
Multi-Commodity Routing
Theory of computation~Distributed algorithms
31:1-31:16
Regular Paper
Mohsen
Ghaffari
Mohsen Ghaffari
ETH Zurich, Switzerland
Jason
Li
Jason Li
Carnegie Mellon University, USA, http://cs.cmu.edu/~jmli
10.4230/LIPIcs.DISC.2018.31
Noga Alon and Joel H Spencer. The probabilistic method. John Wiley &Sons, 2004.
John Augustine, Gopal Pandurangan, Peter Robinson, Scott Roche, and Eli Upfal. Enabling robust and efficient distributed computation in dynamic peer-to-peer networks. In Foundations of Computer Science (FOCS), 2015 IEEE 56th Annual Symposium on, pages 350-369. IEEE, 2015.
Baruch Awerbuch and Christian Scheideler. The hyperring: a low-congestion deterministic data structure for distributed environments. In Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pages 318-327. Society for Industrial and Applied Mathematics, 2004.
Ruben Becker, Andreas Karrenbauer, Sebastian Krinninger, and Christoph Lenzen. Near-optimal approximate shortest paths and transshipment in distributed and streaming models. arXiv preprint arXiv:1607.05127, 2016.
Soumyottam Chatterjee, Reza Fathi, Gopal Pandurangan, and Nguyen Dinh Pham. Fast and efficient distributed computation of hamiltonian cycles in random graphs. arXiv preprint arXiv:1804.08819, 2018.
Colin Cooper and Alan Frieze. Random walks on random graphs. In International Conference on Nano-Networks, pages 95-106. Springer, 2008.
Don Coppersmith, Prabhakar Raghavan, and Martin Tompa. Parallel graph algorithms that are efficient on average. In Foundations of Computer Science, 1987., 28th Annual Symposium on, pages 260-269. IEEE, 1987.
David Culler, Richard Karp, David Patterson, Abhijit Sahay, Klaus Erik Schauser, Eunice Santos, Ramesh Subramonian, and Thorsten Von Eicken. Logp: Towards a realistic model of parallel computation. ACM Sigplan Notices, 28(7):1-12, 1993.
Paul Erdös and Alfréd Rényi. On random graphs, i. Publicationes Mathematicae (Debrecen), 6:290-297, 1959.
Carlo Fantozzi, Andrea Pietracaprina, and Geppino Pucci. A general pram simulation scheme for clustered machines. International Journal of Foundations of Computer Science, 14(06):1147-1164, 2003.
Steven Fortune and James Wyllie. Parallelism in random access machines. In Proc. of the Symp. on Theory of Comp. (STOC), pages 114-118. ACM, 1978.
Mohsen Ghaffari and Bernhard Haeupler. Distributed algorithms for planar networks ii: Low-congestion shortcuts, mst, and min-cut. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pages 202-219. Society for Industrial and Applied Mathematics, 2016.
Mohsen Ghaffari, Fabian Kuhn, and Hsin-Hao Su. Distributed mst and routing in almost mixing time. In Proceedings of the ACM Symposium on Principles of Distributed Computing, pages 131-140. ACM, 2017.
Leslie M Goldschlager. A unified approach to models of synchronous parallel machines. In Proc. of the Symp. on Theory of Comp. (STOC), pages 89-94. ACM, 1978.
Richard M Karp. A survey of parallel algorithms for shared-memory machines. Technical report, University of California at Berkeley, 1988.
Richard M Karp, Michael Luby, and F Meyer auf der Heide. Efficient pram simulation on a distributed memory machine. Algorithmica, 16(4-5):517-542, 1996.
K Krzywdziński and Katarzyna Rybarczyk. Distributed algorithms for random graphs. Theoretical Computer Science, 605:95-105, 2015.
Vipin Kumar, Ananth Grama, Anshul Gupta, and George Karypis. Introduction to parallel computing: design and analysis of algorithms, volume 400. Benjamin/Cummings Redwood City, 1994.
Richard E Ladner and Michael J Fischer. Parallel prefix computation. Journal of the ACM (JACM), 27(4):831-838, 1980.
Ching Law and Kai-Yeung Siu. Distributed construction of random expander networks. In INFOCOM 2003. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications. IEEE Societies, volume 3, pages 2133-2143. IEEE, 2003.
Tom Leighton, Bruce Maggs, and Satish Rao. Universal packet routing algorithms. In Foundations of Computer Science, 1988., 29th Annual Symposium on, pages 256-269. IEEE, 1988.
Eythan Levy, Guy Louchard, and Jordi Petit. A distributed algorithm to find hamiltonian cycles in g(n,p) random graphs. In Workshop on Combinatorial and Algorithmic aspects of networking, pages 63-74. Springer, 2004.
Peter Mahlmann and Christian Schindelhauer. Peer-to-peer networks based on random transformations of connected regular undirected graphs. In Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures, pages 155-164. ACM, 2005.
Gopal Pandurangan, Prabhakar Raghavan, and Eli Upfal. Building low-diameter peer-to-peer networks. Selected Areas in Communications, IEEE Journal on, 21(6):995-1002, 2003.
Gopal Pandurangan, Peter Robinson, and Amitabh Trehan. Dex: self-healing expanders. In Parallel and Distributed Processing Symposium, 2014 IEEE 28th International, pages 702-711. IEEE, 2014.
Gopal Pandurangan and Amitabh Trehan. Xheal: localized self-healing using expanders. In Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pages 301-310. ACM, 2011.
David Peleg. Distributed Computing: A Locality-sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2000.
Richard Peng and Daniel A Spielman. An efficient parallel solver for sdd linear systems. In Proceedings of the forty-sixth annual ACM symposium on Theory of computing, pages 333-342. ACM, 2014.
Andrea Pietracaprina and Geppino Pucci. The complexity of deterministic pram simulation on distributed memory machines. Theory of Computing Systems, 30(3):231-247, 1997.
Walter J Savitch and Michael J Stimson. Time bounded random access machines with parallel processing. Journal of the ACM (JACM), 26(1):103-118, 1979.
Jonah Sherman. Nearly maximum flows in nearly linear time. In Foundations of Computer Science (FOCS), 2013 IEEE 54th Annual Symposium on, pages 263-269. IEEE, 2013.
Jonah Sherman. Generalized preconditioning and undirected minimum-cost flow. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 772-780. SIAM, 2017.
Ion Stoica, Robert Morris, David Karger, M Frans Kaashoek, and Hari Balakrishnan. Chord: A scalable peer-to-peer lookup service for internet applications. ACM SIGCOMM Computer Communication Review, 31(4):149-160, 2001.
Leslie G Valiant. A bridging model for parallel computation. Communications of the ACM, 33(8):103-111, 1990.
Mohsen Ghaffari and Jason Li
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Time-Message Trade-Offs in Distributed Algorithms
This paper focuses on showing time-message trade-offs in distributed algorithms for fundamental problems such as leader election, broadcast, spanning tree (ST), minimum spanning tree (MST), minimum cut, and many graph verification problems. We consider the synchronous CONGEST distributed computing model and assume that each node has initial knowledge of itself and the identifiers of its neighbors - the so-called KT_1 model - a well-studied model that also naturally arises in many applications. Recently, it has been established that one can obtain (almost) singularly optimal algorithms, i.e., algorithms that have simultaneously optimal time and message complexity (up to polylogarithmic factors), for many fundamental problems in the standard KT_0 model (where nodes have only local knowledge of themselves and not their neighbors). The situation is less clear in the KT_1 model. In this paper, we present several new distributed algorithms in the KT_1 model that trade off between time and message complexity.
Our distributed algorithms are based on a uniform and general approach which involves constructing a sparsified spanning subgraph of the original graph - called a danner - that trades off the number of edges with the diameter of the sparsifier. In particular, a key ingredient of our approach is a distributed randomized algorithm that, given a graph G and any delta in [0,1], with high probability constructs a danner that has diameter O~(D + n^{1-delta}) and O~(min{m,n^{1+delta}}) edges in O~(n^{1-delta}) rounds while using O~(min{m,n^{1+delta}}) messages, where n, m, and D are the number of nodes, edges, and the diameter of G, respectively. Using our danner construction, we present a family of distributed randomized algorithms for various fundamental problems that exhibit a trade-off between message and time complexity and that improve over previous results. Specifically, we show the following results (all hold with high probability) in the KT_1 model, which subsume and improve over prior bounds in the KT_1 model (King et al., PODC 2014 and Awerbuch et al., JACM 1990) and the KT_0 model (Kutten et al., JACM 2015, Pandurangan et al., STOC 2017 and Elkin, PODC 2017):
1) Leader Election, Broadcast, and ST. These problems can be solved in O~(D+n^{1-delta}) rounds using O~(min{m,n^{1+delta}}) messages for any delta in [0,1].
2) MST and Connectivity. These problems can be solved in O~(D+n^{1-delta}) rounds using O~(min{m,n^{1+delta}}) messages for any delta in [0,0.5]. In particular, for delta = 0.5 we obtain a distributed MST algorithm that runs in optimal O~(D+sqrt{n}) rounds and uses O~(min{m,n^{3/2}}) messages. We note that this improves over the singularly optimal algorithm in the KT_0 model that uses O~(D+sqrt{n}) rounds and O~(m) messages.
3) Minimum Cut. O(log n)-approximate minimum cut can be solved in O~(D+n^{1-delta}) rounds using O~(min{m,n^{1+delta}}) messages for any delta in [0,0.5].
4) Graph Verification Problems such as Bipartiteness, Spanning Subgraph etc. These can be solved in O~(D+n^{1-delta}) rounds using O~(min{m,n^{1+delta}}) messages for any delta in [0,0.5].
Randomized Algorithm
KT_1 Model
Sparsifier
MST
Singular Optimality
Theory of computation~Distributed algorithms
32:1-32:18
Regular Paper
Supported, in part, by NSF awards CCF-1527867, CCF-1540512, IIS-1633720, CCF-1717075, and BSF award 2016419.
Robert
Gmyr
Robert Gmyr
Department of Computer Science, University of Houston, USA
Gopal
Pandurangan
Gopal Pandurangan
Department of Computer Science, University of Houston, USA
10.4230/LIPIcs.DISC.2018.32
Donald Aingworth, Chandra Chekuri, Piotr Indyk, and Rajeev Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM J. Comput., 28(4):1167-1181, 1999. URL: http://dx.doi.org/10.1137/S0097539796303421.
http://dx.doi.org/10.1137/S0097539796303421
Baruch Awerbuch, Oded Goldreich, David Peleg, and Ronen Vainish. A trade-off between information and communication in broadcast protocols. J. ACM, 37(2):238-256, 1990.
Larry Carter and Mark N. Wegman. Universal classes of hash functions. J. Comput. Syst. Sci., 18(2):143-154, 1979.
Yongwook Choi, Gopal Pandurangan, Maleq Khan, and V. S. Anil Kumar. Energy-optimal distributed algorithms for minimum spanning trees. IEEE Journal on Selected Areas in Communications, 27(7):1297-1304, 2009.
Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. SIAM J. Comput., 41(5):1235-1265, 2012.
Dorit Dor, Shay Halperin, and Uri Zwick. All-pairs almost shortest paths. SIAM J. Comput., 29(5):1740-1759, 2000. URL: http://dx.doi.org/10.1137/S0097539797327908.
http://dx.doi.org/10.1137/S0097539797327908
Michael Elkin. A simple deterministic distributed MST algorithm, with near-optimal time and message complexities. In Proceedings of the 2017 ACM Symposium on Principles of Distributed Computing (PODC), pages 157-163, 2017.
Uriel Feige, David Peleg, Prabhakar Raghavan, and Eli Upfal. Randomized broadcast in networks. Random Struct. Algorithms, 1(4):447-460, 1990. URL: http://dx.doi.org/10.1002/rsa.3240010406.
http://dx.doi.org/10.1002/rsa.3240010406
Robert G. Gallager, Pierre A. Humblet, and Philip M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst., 5(1):66-77, 1983. URL: http://dx.doi.org/10.1145/357195.357200.
http://dx.doi.org/10.1145/357195.357200
J. Garay, S. Kutten, and D. Peleg. A sublinear time distributed algorithm for minimum-weight spanning trees. SIAM Journal on Computing, 27(1):302-316, February 1998.
Mohsen Ghaffari and Fabian Kuhn. Distributed minimum cut approximation. In Distributed Computing - 27th International Symposium, DISC 2013, Jerusalem, Israel, October 14-18, 2013. Proceedings, pages 1-15, 2013.
Bernhard Haeupler, D. Ellis Hershkowitz, and David Wajc. Round- and message-optimal distributed graph algorithms. In PODC, 2018.
James W. Hegeman, Gopal Pandurangan, Sriram V. Pemmaraju, Vivek B. Sardeshmukh, and Michele Scquizzato. Toward optimal bounds in the congested clique: graph connectivity and MST. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (PODC), pages 91-100, 2015.
David R. Karger. Random sampling in cut, flow, and network design problems. Math. Oper. Res., 24(2):383-413, 1999.
Maleq Khan, Gopal Pandurangan, and V. S. Anil Kumar. Distributed algorithms for constructing approximate minimum spanning trees in wireless sensor networks. IEEE Trans. Parallel Distrib. Syst., 20(1):124-139, 2009.
Valerie King, Shay Kutten, and Mikkel Thorup. Construction and impromptu repair of an MST in a distributed network with o(m) communication. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC 2015, Donostia-San Sebastián, Spain, July 21 - 23, 2015, pages 71-80, 2015. URL: http://dx.doi.org/10.1145/2767386.2767405.
http://dx.doi.org/10.1145/2767386.2767405
Hartmut Klauck, Danupon Nanongkai, Gopal Pandurangan, and Peter Robinson. Distributed computation of large-scale graph problems. In Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 391-410, 2015.
Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. On the complexity of universal leader election. J. ACM, 62(1), 2015.
Ali Mashreghi and Valerie King. Time-communication trade-offs for minimum spanning tree construction. In Proceedings of the 18th International Conference on Distributed Computing and Networking, Hyderabad, India, January 5-7, 2017, page 8, 2017. URL: http://dl.acm.org/citation.cfm?id=3007775.
http://dl.acm.org/citation.cfm?id=3007775
Michael Mitzenmacher and Eli Upfal. Probability and computing - randomized algorithms and probabilistic analysis. Cambridge University Press, 2005.
Danupon Nanongkai and Hsin-Hao Su. Almost-tight distributed minimum cut algorithms. In Distributed Computing - 28th International Symposium, DISC 2014, Austin, TX, USA, October 12-15, 2014. Proceedings, pages 439-453, 2014.
Gopal Pandurangan. Distributed network algorithms. Draft, 2018. URL: https://sites.google.com/site/gopalpandurangan/dna.
https://sites.google.com/site/gopalpandurangan/dna
Gopal Pandurangan and Maleq Khan. Theory of communication networks. In Algorithms and Theory of Computation Handbook. CRC Press, 2009.
Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. Fast distributed algorithms for connectivity and MST in large graphs. In Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2016, Asilomar State Beach/Pacific Grove, CA, USA, July 11-13, 2016, pages 429-438, 2016.
Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. A time- and message-optimal distributed algorithm for minimum spanning trees. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, Montreal, QC, Canada, June 19-23, 2017, pages 743-756, 2017. URL: http://dx.doi.org/10.1145/3055399.3055449.
http://dx.doi.org/10.1145/3055399.3055449
Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. On the distributed complexity of large-scale graph computations. In Proceedings of the 30th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA, 2018.
D. Peleg. Distributed Computing: A Locality Sensitive Approach. SIAM, 2000.
Jeanette P. Schmidt, Alan Siegel, and Aravind Srinivasan. Chernoff-hoeffding bounds for applications with limited independence. SIAM J. Discrete Math., 8(2):223-250, 1995.
Robert Gmyr and Gopal Pandurangan
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Faster Distributed Shortest Path Approximations via Shortcuts
A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms, however, is Omega~(sqrt{n}), regardless of the network topology, even on nice networks with a (poly)logarithmic network diameter D. While this is known to be necessary for some pathological networks, most topologies of interest are arguably not of this type.
We give the first distributed approximation algorithms for shortest paths problems that adjust to the topology they are run on, thus achieving significantly faster running times on many topologies of interest. The running time of our algorithms depends on and is close to Q, where Q is the quality of the best shortcut that exists for the given topology. While Q = Theta~(sqrt{n} + D) for pathological worst-case topologies, many topologies of interest have Q = Theta~(D), which results in near instance optimal running times for our algorithm, given the trivial Omega(D) lower bound.
The problems we consider are as follows:
- an approximate shortest path tree and SSSP distances,
- a polylogarithmic size distance label for every node such that from the labels of any two nodes alone one can determine their distance (approximately), and
- an (approximately) optimal flow for the transshipment problem.
Our algorithms have a tunable tradeoff between running time and approximation ratio. Our fastest algorithms have an arbitrarily good polynomial approximation guarantee and an essentially optimal O~(Q) running time. On the other end of the spectrum, we achieve polylogarithmic approximations in O~(Q * n^epsilon) rounds for any epsilon > 0. It seems likely that eventually, our non-trivial approximation algorithms for the SSSP tree and transshipment problem can be bootstrapped to give fast Q * 2^O(sqrt{log n log log n}) round (1+epsilon)-approximation algorithms using a recent result by Becker et al.
Distributed Graph Algorithms
Shortest Path
Shortcuts
Theory of computation~Shortest paths
Theory of computation~Distributed algorithms
Theory of computation~Approximation algorithms analysis
33:1-33:14
Regular Paper
https://arxiv.org/abs/1802.03671
Bernhard
Haeupler
Bernhard Haeupler
Carnegie Mellon University, USA, http://cs.cmu.edu/~haeupler
Supported in part by NSF grants CCF-1527110, CCF-1618280 and NSF CAREER award CCF-1750808.
Jason
Li
Jason Li
Carnegie Mellon University, USA, http://cs.cmu.edu/~jmli
10.4230/LIPIcs.DISC.2018.33
Ittai Abraham, Cyril Gavoille, Anupam Gupta, Ofer Neiman, and Kunal Talwar. Cops, robbers, and threatening skeletons: Padded decomposition for minor-free graphs. In Proceedings of the 46th Annual ACM Symposium on Theory of Computing, pages 79-88. ACM, 2014.
Noga Alon, Richard M Karp, David Peleg, and Douglas West. A graph-theoretic game and its application to the k-server problem. SIAM Journal on Computing, 24(1):78-100, 1995.
Baruch Awerbuch, Bonnie Berger, Lenore Cowen, and David Peleg. Low-diameter graph decomposition is in nc. In Scandinavian Workshop on Algorithm Theory, pages 83-93. Springer, 1992.
Yair Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. In Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on, pages 184-193. IEEE, 1996.
Ruben Becker, Andreas Karrenbauer, Sebastian Krinninger, and Christoph Lenzen. Near-optimal approximate shortest paths and transshipment in distributed and streaming models. In International Symposium on Distributed Computing, 2017.
Guy E Blelloch, Anupam Gupta, Ioannis Koutis, Gary L Miller, Richard Peng, and Kanat Tangwongsan. Nearly-linear work parallel sdd solvers, low-diameter decomposition, and low-stretch subgraphs. Theory of Computing Systems, 55(3):521-554, 2014.
Michael Elkin and Ofer Neiman. Distributed strong diameter network decomposition. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, pages 211-216. ACM, 2016.
Mohsen Ghaffari and Bernhard Haeupler. Distributed algorithms for planar networks ii: Low-congestion shortcuts, mst, and min-cut. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pages 202-219. Society for Industrial and Applied Mathematics, 2016.
Bernhard Haeupler, Taisuke Izumi, and Goran Zuzic. Low-congestion shortcuts without embedding. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, pages 451-460. ACM, 2016.
Bernhard Haeupler, Taisuke Izumi, and Goran Zuzic. Near-optimal low-congestion shortcuts on bounded parameter graphs. In International Symposium on Distributed Computing, pages 158-172. Springer, 2016.
Bernhard Haeupler, Goran Zuzic, and Jason Li. Low-congestion shortcuts for any minor closed family. In personal communications, 2017.
Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai. An almost-tight distributed algorithm for computing single-source shortest paths. In Proceedings of the ACM Symposium on Theory of Computing, 2016.
Shay Kutten and David Peleg. Fast distributed construction of k-dominating sets and applications. In Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing, pages 238-251. ACM, 1995.
Christoph Lenzen and Boaz Patt-Shamir. Fast partial distance estimation and applications. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, pages 153-162. ACM, 2015.
Nathan Linial and Michael E Saks. Decomposing graphs into regions of small diameter. In SODA, volume 91, pages 320-330, 1991.
Gary L Miller, Richard Peng, and Shen Chen Xu. Parallel graph decompositions using random shifts. In Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures, pages 196-203. ACM, 2013.
Danupon Nanongkai. Distributed approximation algorithms for weighted shortest paths. In Proceedings of the ACM Symposium on Theory of Computing, pages 565-573, 2014.
Danupon Nanongkai and Hsin-Hao Su. Almost-tight distributed minimum cut algorithms. In International Symposium on Distributed Computing, pages 439-453. Springer, 2014.
Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. SIAM Journal on Computing, 41(5):1235-1265, 2012.
Bernhard Haeupler and Jason Li
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
A Lower Bound for Adaptively-Secure Collective Coin-Flipping Protocols
In 1985, Ben-Or and Linial (Advances in Computing Research '89) introduced the collective coin-flipping problem, where n parties communicate via a single broadcast channel and wish to generate a common random bit in the presence of adaptive Byzantine corruptions. In this model, the adversary can decide to corrupt a party in the course of the protocol as a function of the messages seen so far. They showed that the majority protocol, in which each player sends a random bit and the output is the majority value, tolerates O(sqrt n) adaptive corruptions. They conjectured that this is optimal for such adversaries.
We prove that the majority protocol is optimal (up to a poly-logarithmic factor) among all protocols in which each party sends a single, possibly long, message.
Previously, such a lower bound was known for protocols in which parties are allowed to send only a single bit (Lichtenstein, Linial, and Saks, Combinatorica '89), or for symmetric protocols (Goldwasser, Kalai, and Park, ICALP '15).
Coin flipping
adaptive corruptions
byzantine faults
lower bound
Theory of computation~Complexity theory and logic
34:1-34:16
Regular Paper
Yael
Tauman Kalai
Yael Tauman Kalai
Microsoft Research, 1 Memorial Dr, Cambridge, MA 02142, USA
Ilan
Komargodski
Ilan Komargodski
Cornell Tech, 2 W Loop Rd, New York, NY 10044, USA
Supported in part by a Packard Foundation Fellowship and by an AFOSR grant FA9550-15-1-0262.
Ran
Raz
Ran Raz
Department of Computer Science, Princeton University, Princeton, NJ 08544, USA
Research supported by the Simons Collaboration on Algorithms and Geometry and by the National Science Foundation grants No. CCF-1714779 and CCF-1412958.
10.4230/LIPIcs.DISC.2018.34
Miklós Ajtai and Nathan Linial. The influence of large coalitions. Combinatorica, 13(2):129-145, 1993.
Bar Alon and Eran Omri. Almost-optimally fair multiparty coin-tossing with nearly three-quarters malicious. In Theory of Cryptography - 14th International Conference, TCC 2016-B, pages 307-335, 2016.
Noga Alon and Moni Naor. Coin-flipping games immune against linear-sized coalitions. SIAM J. Comput., 22(2):403-417, 1993.
Noga Alon and Joel Spencer. The Probabilistic Method. John Wiley, third edition, 2008.
Amos Beimel, Iftach Haitner, Nikolaos Makriyannis, and Eran Omri. Tighter bounds on multi-party coin flipping, via augmented weak martingales and di erentially private sampling. Electronic Colloquium on Computational Complexity (ECCC), 24:168, 2017.
Amos Beimel, Eran Omri, and Ilan Orlov. Protocols for multiparty coin toss with a dishonest majority. J. Cryptology, 28(3):551-600, 2015.
Michael Ben-Or and Nathan Linial. Collective coin flipping. Advances in Computing Research, 5:91-115, 1989.
Ravi B. Boppana and Babu O. Narayanan. The biased coin problem. SIAM J. Discrete Math., 9(1):29-36, 1996.
Niv Buchbinder, Iftach Haitner, Nissan Levi, and Eliad Tsfadia. Fair coin flipping: Tighter analysis and the many-party case. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pages 2580-2600. SIAM, 2017.
Richard Cleve. Limits on the security of coin flips when half the processors are faulty (extended abstract). In Juris Hartmanis, editor, Proceedings of the 18th Annual ACM Symposium on Theory of Computing, pages 364-369. ACM, 1986.
Richard Cleve and Russell Impagliazzo. Martingales, collective coin flipping and discrete control processes (extended abstract), 1993. Unpublished manuscript.
Yevgeniy Dodis. Impossibility of black-box reduction from non-adaptively to adaptively secure coin-flipping. Electronic Colloquium on Computational Complexity (ECCC), 7(39), 2000.
Devdatt P. Dubhashi and Alessandro Panconesi. Concentration of Measure for the Analysis of Randomized Algorithms. Cambridge University Press, 2009. URL: http://dx.doi.org/10.1017/CBO9780511581274.
http://dx.doi.org/10.1017/CBO9780511581274
Uriel Feige. Noncryptographic selection protocols. In 40th Annual Symposium on Foundations of Computer Science, FOCS, pages 142-153, 1999.
Shafi Goldwasser, Yael Tauman Kalai, and Sunoo Park. Adaptively secure coin-flipping, revisited. In 42nd International Colloquium on Automata, Languages and Programming,, ICALP, pages 663-674, 2015.
Iftach Haitner and Eliad Tsfadia. An almost-optimally fair three-party coin-flipping protocol. SIAM J. Comput., 46(2):479-542, 2017.
Jeff Kahn, Gil Kalai, and Nathan Linial. The influence of variables on boolean functions (extended abstract). In 29th Annual Symposium on Foundations of Computer Science, FOCS, pages 68-80, 1988.
Yael Tauman Kalai and Ilan Komargodski. Compressing communication in distributed protocols. In Distributed Computing - 29th International Symposium, DISC, pages 467-479, 2015.
David Lichtenstein, Nathan Linial, and Michael E. Saks. Some extremal problems arising form discrete control processes. Combinatorica, 9(3):269-287, 1989.
Tal Moran, Moni Naor, and Gil Segev. An optimally fair coin toss. J. Cryptology, 29(3):491-513, 2016.
Alexander Russell, Michael E. Saks, and David Zuckerman. Lower bounds for leader election and collective coin-flipping in the perfect information model. SIAM J. Comput., 31(6):1645-1662, 2002.
Michael E. Saks. A robust noncryptographic protocol for collective coin flipping. SIAM J. Discrete Math., 2(2):240-244, 1989.
Yael T. Kalai, Ilan Komargodski, and Ran Raz
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Adapting Local Sequential Algorithms to the Distributed Setting
It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number of colors. Surprisingly, this well known idea was never formally stated as a unified framework. In this paper we aim to define a robust family of local sequential algorithms which can be easily adapted to the distributed setting. We then develop new tools to further enhance these algorithms, achieving state of the art results for fundamental problems.
We define a simple class of greedy-like algorithms which we call orderless-local algorithms. We show that given a legal c-coloring of the graph, every algorithm in this family can be converted into a distributed algorithm running in O(c) communication rounds in the CONGEST model. We show that this family is indeed robust as both the method of conditional expectations and the unconstrained submodular maximization algorithm of Buchbinder et al. [Niv Buchbinder et al., 2015] can be expressed as orderless-local algorithms for local utility functions - Utility functions which have a strong local nature to them.
We use the above algorithms as a base for new distributed approximation algorithms for the weighted variants of some fundamental problems: Max k-Cut, Max-DiCut, Max 2-SAT and correlation clustering. We develop algorithms which have the same approximation guarantees as their sequential counterparts, up to a constant additive epsilon factor, while achieving an O(log^* n) running time for deterministic algorithms and O(epsilon^{-1}) running time for randomized ones. This improves exponentially upon the currently best known algorithms.
Distributed
Approximation Algorithms
Derandomization
Max-Cut
Theory of computation~Distributed algorithms
35:1-35:17
Regular Paper
This work was supported by JST ERATO Grant Number JPMJER1201, Japan
A full version of the paper is available at https://arxiv.org/abs/1711.10155.
Ken-ichi
Kawarabayashi
Ken-ichi Kawarabayashi
National Institute of Informatics, Tokyo, Japan
Gregory
Schwartzman
Gregory Schwartzman
National Institute of Informatics, Tokyo, Japan
10.4230/LIPIcs.DISC.2018.35
Kook Jin Ahn, Graham Cormode, Sudipto Guha, Andrew McGregor, and Anthony Wirth. Correlation clustering in data streams. In ICML, volume 37 of JMLR Workshop and Conference Proceedings, pages 2237-2246. JMLR.org, 2015.
Nir Ailon, Moses Charikar, and Alantha Newman. Aggregating inconsistent information: Ranking and clustering. J. ACM, 55(5):23:1-23:27, 2008.
Per Austrin. Balanced max 2-sat might not be the hardest. In STOC, pages 189-197. ACM, 2007.
Nikhil Bansal, Avrim Blum, and Shuchi Chawla. Correlation clustering. In FOCS, page 238. IEEE Computer Society, 2002.
Reuven Bar-Yehuda, Keren Censor-Hillel, Mohsen Ghaffari, and Gregory Schwartzman. Distributed approximation of maximum independent set and maximum matching. In PODC, pages 165-174. ACM, 2017.
Reuven Bar-Yehuda, Keren Censor-Hillel, and Gregory Schwartzman. A distributed (2 + ε)-approximation for vertex cover in o(log Δ / ε log log Δ) rounds. J. ACM, 64(3):23:1-23:11, 2017.
Surender Baswana and Sandeep Sen. A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs. Random Struct. Algorithms, 30(4):532-563, 2007.
Ran Ben-Basat, Ken-ichi Kawarabayashi, and Gregory Schwartzman. Parameterized distributed algorithms. CoRR, abs/1807.04900, 2018. URL: http://arxiv.org/abs/1807.04900.
http://arxiv.org/abs/1807.04900
Allan Borodin, Morten N. Nielsen, and Charles Rackoff. (incremental) priority algorithms. In SODA, pages 752-761. ACM/SIAM, 2002.
Niv Buchbinder, Moran Feldman, Joseph Naor, and Roy Schwartz. A tight linear time (1/2)-approximation for unconstrained submodular maximization. SIAM J. Comput., 44(5):1384-1402, 2015. URL: http://dx.doi.org/10.1137/130929205.
http://dx.doi.org/10.1137/130929205
Keren Censor-Hillel, Elad Haramaty, and Zohar S. Karnin. Optimal dynamic distributed MIS. In PODC, pages 217-226. ACM, 2016.
Keren Censor-Hillel, Rina Levy, and Hadas Shachnai. Fast distributed approximation for max-cut. In Algorithms for Sensor Systems, 13th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2017, Vienna, Austria, September 7-8, 2017, Revised Selected Papers, volume 10718 of Lecture Notes in Computer Science, pages 41-56. Springer, 2017.
Moses Charikar, Venkatesan Guruswami, and Anthony Wirth. Clustering with qualitative information. J. Comput. Syst. Sci., 71(3):360-383, 2005.
Shuchi Chawla, Konstantin Makarychev, Tselil Schramm, and Grigory Yaroslavtsev. Near optimal LP rounding algorithm for correlationclustering on complete and complete k-partite graphs. In STOC, pages 219-228. ACM, 2015.
Erik D. Demaine, Dotan Emanuel, Amos Fiat, and Nicole Immorlica. Correlation clustering in general weighted graphs. Theor. Comput. Sci., 361(2-3):172-187, 2006.
Uriel Feige and Michel X. Goemans. Aproximating the value of two prover proof systems, with applications to MAX 2sat and MAX DICUT. In ISTCS, pages 182-189. IEEE Computer Society, 1995.
Manuela Fischer, Mohsen Ghaffari, and Fabian Kuhn. Deterministic distributed edge-coloring via hypergraph maximal matching. In FOCS, pages 180-191. IEEE Computer Society, 2017.
Robert G. Gallager, Pierre A. Humblet, and Philip M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst., 5(1):66-77, 1983.
M. R. Garey, David S. Johnson, and Larry J. Stockmeyer. Some simplified np-complete graph problems. Theor. Comput. Sci., 1(3):237-267, 1976. URL: http://dx.doi.org/10.1016/0304-3975(76)90059-1.
http://dx.doi.org/10.1016/0304-3975(76)90059-1
Mohsen Ghaffari, David G. Harris, and Fabian Kuhn. On derandomizing local distributed algorithms. CoRR, abs/1711.02194, 2017.
Mohsen Ghaffari, Fabian Kuhn, and Yannic Maus. On the complexity of local distributed graph problems. In STOC, pages 784-797. ACM, 2017.
Ioannis Giotis and Venkatesan Guruswami. Correlation clustering with a fixed number of clusters. Theory of Computing, 2(13):249-266, 2006.
Michel X. Goemans and David P. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM, 42(6):1115-1145, 1995. URL: http://dx.doi.org/10.1145/227683.227684.
http://dx.doi.org/10.1145/227683.227684
Johan Håstad. Some optimal inapproximability results. J. ACM, 48(4):798-859, 2001.
Juho Hirvonen, Joel Rybicki, Stefan Schmid, and Jukka Suomela. Large cuts with local algorithms on triangle-free graphs. CoRR, abs/1402.2543, 2014.
Satyen Kale and C. Seshadhri. Combinatorial approximation algorithms for maxcut using random walks. In ICS, pages 367-388. Tsinghua University Press, 2011.
Richard M. Karp. Reducibility among combinatorial problems. In Complexity of Computer Computations, The IBM Research Symposia Series, pages 85-103. Plenum Press, New York, 1972.
Subhash Khot, Guy Kindler, Elchanan Mossel, and Ryan O'Donnell. Optimal inapproximability results for MAX-CUT and other 2-variable csps? SIAM J. Comput., 37(1):319-357, 2007.
Fabian Kuhn. Weak graph colorings: distributed algorithms and applications. In SPAA, pages 138-144. ACM, 2009.
Reut Levi and Moti Medina. A (centralized) local guide. Bulletin of EATCS, 2(122), 2017.
Michael Lewin, Dror Livnat, and Uri Zwick. Improved rounding techniques for the MAX 2-sat and MAX DI-CUT problems. In IPCO, volume 2337 of Lecture Notes in Computer Science, pages 67-82. Springer, 2002.
Nathan Linial. Locality in distributed graph algorithms. SIAM J. Comput., 21(1):193-201, 1992.
Shiro Matuura and Tomomi Matsui. 0.863-approximation algorithm for MAX DICUT. In RANDOM-APPROX, volume 2129 of Lecture Notes in Computer Science, pages 138-146. Springer, 2001.
Matthias Poloczek, Georg Schnitger, David P. Williamson, and Anke van Zuylen. Greedy algorithms for the maximum satisfiability problem: Simple algorithms and inapproximability bounds. SIAM J. Comput., 46(3):1029-1061, 2017.
Ronitt Rubinfeld, Gil Tamir, Shai Vardi, and Ning Xie. Fast local computation algorithms. In ICS, pages 223-238. Tsinghua University Press, 2011.
Chaitanya Swamy. Correlation clustering: maximizing agreements via semidefinite programming. In SODA, pages 526-527. SIAM, 2004.
Luca Trevisan. Max cut and the smallest eigenvalue. SIAM J. Comput., 41(6):1769-1786, 2012.
Luca Trevisan, Gregory B. Sorkin, Madhu Sudan, and David P. Williamson. Gadgets, approximation, and linear programming. SIAM J. Comput., 29(6):2074-2097, 2000.
Ken-ichi Kawarabayashi and Gregory Schwartzman
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Strong Separations Between Broadcast and Authenticated Channels
In the theory of distributed systems and cryptography one considers a setting with n parties, (often) connected via authenticated bilateral channels, who want to achieve a certain goal even if some fraction of the parties is dishonest. A classical goal of this type is to construct a broadcast channel. A broadcast channel guarantees that all honest recipients get the same value v (consistency) and, if the sender is honest, that v is the sender's input (validity). Lamport et al. showed that it is possible to construct broadcast if and only if the fraction of cheaters is less than a third.
A natural question, first raised by Lamport, is whether there are weaker, still useful primitives achievable from authenticated channels. He proposed weak broadcast, where the validity condition must hold only if all parties are honest, and showed that it can be achieved with an unbounded number of protocol rounds, while broadcast cannot, suggesting that weak broadcast is in a certain sense weaker than broadcast.
The purpose of this paper is to deepen the investigation of the separation between broadcast and authenticated channels. This is achieved by proving the following results. First, we prove a stronger impossibility result for 3-party broadcast. Even if two of the parties can broadcast, one can not achieve broadcast for the third party. Second, we prove a strong separation between authenticated channels and broadcast by exhibiting a new primitive, called XOR-cast, which satisfies two conditions: (1) XOR-cast is strongly unachievable (even with small error probability) from authenticated channels (which is not true for weak broadcast), and (2) broadcast is strongly unachievable from XOR-cast (and authenticated channels). This demonstrates that the hierarchy of primitives has a more complex structure than previously known. Third, we prove a strong separation between weak broadcast and broadcast which is not implied by Lamport's results. The proofs of these results requires the generalization of known techniques for impossibility proofs.
cryptography
multi-party computation
broadcast
impossibility
Theory of computation~Cryptographic protocols
36:1-36:17
Regular Paper
Julian
Loss
Julian Loss
Ruhr University Bochum, Germany
https://orcid.org/0000-0002-7979-3810
Ueli
Maurer
Ueli Maurer
ETH Zurich, Switzerland
Daniel
Tschudi
Daniel Tschudi
Aarhus University, Denmark
https://orcid.org/0000-0001-6188-1049
Author was supported by advanced ERC grant MPCPRO.
10.4230/LIPIcs.DISC.2018.36
Jeffrey Considine, Matthias Fitzi, Matthew K. Franklin, Leonid A. Levin, Ueli M. Maurer, and David Metcalf. Byzantine agreement given partial broadcast. Journal of Cryptology, 18(3):191-217, jul 2005.
Michael J. Fischer, Nancy A. Lynch, and Michael Merritt. Easy impossibility proofs for distributed consensus problems. In Michael A. Malcolm and H. Raymond Strong, editors, 4th ACM Symposium Annual on Principles of Distributed Computing, pages 59-70, Minaki, Ontario, Canada, aug 5-7, 1985. Association for Computing Machinery.
Matthias Fitzi, Daniel Gottesman, Martin Hirt, Thomas Holenstein, and Adam Smith. Detectable byzantine agreement secure against faulty majorities. In Aleta Ricciardi, editor, 21st ACM Symposium Annual on Principles of Distributed Computing, pages 118-126, Monterey, California, USA, jul 21-24, 2002. Association for Computing Machinery.
Matthias Fitzi and Ueli M. Maurer. From partial consistency to global broadcast. In 32nd Annual ACM Symposium on Theory of Computing, pages 494-503, Portland, Oregon, USA, may 21-23, 2000. ACM Press.
Ronald L. Graham and Andrew Chi-Chih Yao. On the improbability of reaching byzantine agreements (preliminary version). In 21st Annual ACM Symposium on Theory of Computing, pages 467-478, Seattle, Washington, USA, may 15-17, 1989. ACM Press.
Martin Hirt, Ueli Maurer, and Pavel Raykov. Broadcast amplification. In Yehuda Lindell, editor, TCC 2014: 11th Theory of Cryptography Conference, volume 8349 of Lecture Notes in Computer Science, pages 419-439, San Diego, CA, USA, feb 24-26, 2014. Springer, Berlin, Germany. URL: http://dx.doi.org/10.1007/978-3-642-54242-8_18.
http://dx.doi.org/10.1007/978-3-642-54242-8_18
Martin Hirt and Ueli M. Maurer. Player simulation and general adversary structures in perfect multiparty computation. Journal of Cryptology, 13(1):31-60, 2000. Extended abstract in Proc. 16th of ACM PODC '97.
Martin Hirt and Daniel Tschudi. Efficient general-adversary multi-party computation. In Kazue Sako and Palash Sarkar, editors, Advances in Cryptology - ASIACRYPT 2013, Part II, volume 8270 of Lecture Notes in Computer Science, pages 181-200, Bengalore, India, dec 1-5, 2013. Springer, Berlin, Germany. URL: http://dx.doi.org/10.1007/978-3-642-42045-0_10.
http://dx.doi.org/10.1007/978-3-642-42045-0_10
Alexander Jaffe, Thomas Moscibroda, and Siddhartha Sen. On the price of equivocation in byzantine agreement. In Darek Kowalski and Alessandro Panconesi, editors, 31st ACM Symposium Annual on Principles of Distributed Computing, pages 309-318, Funchal, Madeira, Portugal, jul 16-18, 2012. Association for Computing Machinery.
Anna Rochelle Karlin and Andrew Chi-Chih Yao. Probabilistic lower bounds for the byzantine generals problem. unpublished manuscript, 1984.
Leslie Lamport. The weak byzantine generals problem. Journal of the ACM, 30(3):668-676, jul 1983.
Leslie Lamport, Robert Shostak, and Marshall Pease. The byzantine generals problem. ACM Transactions on Programming Languages and Systems (TOPLAS), 4(3):382-401, jul 1982.
Julian Loss, Ueli Maurer, and Daniel Tschudi. Hierarchy of three-party consistency specifications. In 2016 IEEE International Symposium on Information Theory (ISIT), pages 3048-3052. IEEE, 2016.
Ueli Maurer. Towards a theory of consistency primitives. In Rachid Guerraoui, editor, International Symposium on Distributed Computing - DISC 2004, volume 3274 of Lecture Notes in Computer Science, pages 379-389. Springer, Berlin, Germany, 2004.
D. V. S. Ravikant, Venkitasubramaniam Muthuramakrishnan, V. Srikanth, K. Srinathan, and C. Pandu Rangan. On byzantine agreement over (2,3)-uniform hypergraphs. In Rachid Guerraoui, editor, International Symposium on Distributed Computing - DISC 2004, volume 3274 of Lecture Notes in Computer Science, pages 450-464. Springer, Berlin, Germany, Oct 2004.
Pavel Raykov. Broadcast from minicast secure against general adversaries. In Magnús M. Halldórsson, Kazuo Iwama, Naoki Kobayashi, and Bettina Speckmann, editors, ICALP 2015: 42nd International Colloquium on Automata, Languages and Programming, Part II, volume 9135 of Lecture Notes in Computer Science, pages 701-712, Kyoto, Japan, jul 6-10, 2015. Springer, Berlin, Germany. URL: http://dx.doi.org/10.1007/978-3-662-47666-6_56.
http://dx.doi.org/10.1007/978-3-662-47666-6_56
Julian Loss, Ueli Maurer, and Daniel Tschudi
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Broadcast and Minimum Spanning Tree with o(m) Messages in the Asynchronous CONGEST Model
We provide the first asynchronous distributed algorithms to compute broadcast and minimum spanning tree with o(m) bits of communication, in a sufficiently dense graph with n nodes and m edges. For decades, it was believed that Omega(m) bits of communication are required for any algorithm that constructs a broadcast tree. In 2015, King, Kutten and Thorup showed that in the KT1 model where nodes have initial knowledge of their neighbors' identities it is possible to construct MST in O~(n) messages in the synchronous CONGEST model. In the CONGEST model messages are of size O(log n). However, no algorithm with o(m) messages were known for the asynchronous case. Here, we provide an algorithm that uses O(n^{3/2} log^{3/2} n) messages to find MST in the asynchronous CONGEST model. Our algorithm is randomized Monte Carlo and outputs MST with high probability. We will provide an algorithm for computing a spanning tree with O(n^{3/2} log^{3/2} n) messages. Given a spanning tree, we can compute MST with O~(n) messages.
Distributed Computing
Minimum Spanning Tree
Broadcast Tree
Computing methodologies~Distributed algorithms
Mathematics of computing~Graph algorithms
37:1-37:17
Regular Paper
https://arxiv.org/abs/1806.04328
Ali
Mashreghi
Ali Mashreghi
Department of Computer Science, University of Victoria, BC, Canada
Funded with an NSERC grant.
Valerie
King
Valerie King
Department of Computer Science, University of Victoria, BC, Canada
Funded with an NSERC grant.
10.4230/LIPIcs.DISC.2018.37
Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. Graph sketches: sparsification, spanners, and subgraphs. In Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI symposium on Principles of Database Systems, pages 5-14. ACM, 2012.
Baruch Awerbuch. Complexity of network synchronization. Journal of the ACM (JACM), 32(4):804-823, 1985.
Baruch Awerbuch. Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems. In Proceedings of the nineteenth annual ACM symposium on Theory of computing, pages 230-240. ACM, 1987.
Baruch Awerbuch, Oded Goldreich, Ronen Vainish, and David Peleg. A trade-off between information and communication in broadcast protocols. Journal of the ACM (JACM), 37(2):238-256, 1990.
Baruch Awerbuch, Shay Kutten, Yishay Mansour, Boaz Patt-Shamir, and George Varghese. A time-optimal self-stabilizing synchronizer using a phase clock. IEEE Transactions on Dependable and Secure Computing, 4(3), 2007.
Baruch Awerbuch and David Peleg. Network synchronization with polylogarithmic overhead. In Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on, pages 514-522. IEEE, 1990.
Michael Elkin. A faster distributed protocol for constructing a minimum spanning tree. In Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pages 359-368. Society for Industrial and Applied Mathematics, 2004.
Michael Elkin. An unconditional lower bound on the time-approximation trade-off for the distributed minimum spanning tree problem. SIAM Journal on Computing, 36(2):433-456, 2006.
Michael Elkin. Synchronizers, spanners. In Encyclopedia of Algorithms, pages 1-99. Springer, 2008.
Michael Elkin. Distributed exact shortest paths in sublinear time. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, pages 757-770, New York, NY, USA, 2017. ACM. URL: http://dx.doi.org/10.1145/3055399.3055452.
http://dx.doi.org/10.1145/3055399.3055452
Michael Elkin. A simple deterministic distributed mst algorithm, with near-optimal time and message complexities. arXiv preprint arXiv:1703.02411, 2017.
Yuval Emek and Amos Korman. Efficient threshold detection in a distributed environment. In Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pages 183-191. ACM, 2010.
Michalis Faloutsos and Mart Molle. Optimal distributed algorithm for minimum spanning trees revisited. In Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing, pages 231-237. ACM, 1995.
Robert G. Gallager, Pierre A. Humblet, and Philip M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Transactions on Programming Languages and systems (TOPLAS), 5(1):66-77, 1983.
Juan A Garay, Shay Kutten, and David Peleg. A sublinear time distributed algorithm for minimum-weight spanning trees. SIAM Journal on Computing, 27(1):302-316, 1998.
Bruce M Kapron, Valerie King, and Ben Mountjoy. Dynamic graph connectivity in polylogarithmic worst case time. In Proceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms, pages 1131-1142. Society for Industrial and Applied Mathematics, 2013.
Maleq Khan and Gopal Pandurangan. A fast distributed approximation algorithm for minimum spanning trees. In Proceedings of the 20th International Conference on Distributed Computing, DISC'06, pages 355-369, Berlin, Heidelberg, 2006. Springer-Verlag. URL: http://dx.doi.org/10.1007/11864219_25.
http://dx.doi.org/10.1007/11864219_25
Valerie King, Shay Kutten, and Mikkel Thorup. Construction and impromptu repair of an mst in a distributed network with o (m) communication. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, pages 71-80. ACM, 2015.
Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. On the complexity of leader election. Journal of the ACM (JACM), 62(1):7, 2015.
Shay Kutten and David Peleg. Fast distributed construction of k-dominating sets and applications. In Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing, pages 238-251. ACM, 1995.
Ali Mashreghi and Valerie King. Time-communication trade-offs for minimum spanning tree construction. In Proceedings of the 18th International Conference on Distributed Computing and Networking, page 8. ACM, 2017.
Ali Mashreghi and Valerie King. Broadcast and minimum spanning tree with o (m) messages in the asynchronous congest model. arXiv, 2018. URL: http://arxiv.org/abs/1806.04328.
http://arxiv.org/abs/1806.04328
Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. A time-and message-optimal distributed algorithm for minimum spanning trees. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages 743-756. ACM, 2017.
David Peleg and Jeffrey D Ullman. An optimal synchronizer for the hypercube. In Proceedings of the sixth annual ACM Symposium on Principles of distributed computing, pages 77-85. ACM, 1987.
Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. SIAM Journal on Computing, 41(5):1235-1265, 2012.
Gurdip Singh and Arthur J Bernstein. A highly asynchronous minimum spanning tree protocol. Distributed Computing, 8(3):151-161, 1995.
Ali Mashreghi and Valerie King
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Fault-Tolerant Consensus with an Abstract MAC Layer
In this paper, we study fault-tolerant distributed consensus in wireless systems. In more detail, we produce two new randomized algorithms that solve this problem in the abstract MAC layer model, which captures the basic interface and communication guarantees provided by most wireless MAC layers. Our algorithms work for any number of failures, require no advance knowledge of the network participants or network size, and guarantee termination with high probability after a number of broadcasts that are polynomial in the network size. Our first algorithm satisfies the standard agreement property, while our second trades a faster termination guarantee in exchange for a looser agreement property in which most nodes agree on the same value. These are the first known fault-tolerant consensus algorithms for this model. In addition to our main upper bound results, we explore the gap between the abstract MAC layer and the standard asynchronous message passing model by proving fault-tolerant consensus is impossible in the latter in the absence of information regarding the network participants, even if we assume no faults, allow randomized solutions, and provide the algorithm a constant-factor approximation of the network size.
abstract MAC layer
wireless networks
consensus
fault tolerance
Theory of computation~Distributed algorithms
38:1-38:20
Regular Paper
https://www.cas.mcmaster.ca/robinson/random-aml.pdf
Calvin
Newport
Calvin Newport
Georgetown University, Washington, D.C., USA
Calvin Newport acknowledges the support of the National Science Foundation, award number 1733842.
Peter
Robinson
Peter Robinson
McMaster University, Hamilton, Canada
Peter Robinson acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), RGPIN-2018-06322.
10.4230/LIPIcs.DISC.2018.38
Mohssen Abboud, Carole Delporte-Gallet, and Hugues Fauconnier. Agreement without knowing everybody: a first step to dynamicity. In Proceedings of the International Conference on New Technologies in Distributed Systems, 2008.
Marcos Kawazoe Aguilera, Wei Chen, and Sam Toueg. Failure detection and consensus in the crash-recovery model. Distributed computing, 13(2):99-125, 2000.
Eduardo AP Alchieri, Alysson Neves Bessani, Joni da Silva Fraga, and Fabíola Greve. Byzantine consensus with unknown participants. In Proceedings of the International Conference on the Principles of Distributed Systems. Springer, 2008.
Khaled Alekeish and Paul Ezhilchelvan. Consensus in sparse, mobile ad hoc networks. IEEE Transactions on Parallel and Distributed Systems, 23(3):467-474, 2012.
James Aspnes. Fast deterministic consensus in a noisy environment. Journal of Algorithms, 45(1):16-39, 2002.
Hagit Attiya, Alla Gorbach, and Shlomo Moran. Computing in totally anonymous asynchronous shared memory systems. Information and Computation, 173(2):162-183, 2002.
John Augustine, Gopal Pandurangan, Peter Robinson, and Eli Upfal. Distributed agreement in dynamic peer-to-peer networks. J. Comput. Syst. Sci., 81(7):1088-1109, 2015. URL: http://dx.doi.org/10.1016/j.jcss.2014.10.005.
http://dx.doi.org/10.1016/j.jcss.2014.10.005
R. Bar-Yehuda, O. Goldreich, and A. Itai. On the Time Complexity of Broadcast in Radio Networks: an Exponential Gap Between Determinism and Randomization. In Proceedings of the ACM Conference on Distributed Computing, 1987.
Michael Ben-Or. Another advantage of free choice (extended abstract): Completely asynchronous agreement protocols. In Proceedings of the ACM Conference on Distributed Computing, pages 27-30. ACM, 1983.
François Bonnet and Michel Raynal. Anonymous Asynchronous Systems: the Case of Failure Detectors. In Proceedings of the International Conference on Distributed Computing, 2010.
David Cavin, Yoav Sasson, and André Schiper. Consensus with unknown participants or fundamental self-organization. In ADHOC-NOW, 2004.
Tushar Deepak Chandra. Polylog randomized wait-free consensus. In Proceedings of the ACM Conference on Distributed Computing, 1996.
Tushar Deepak Chandra and Sam Toueg. Unreliable failure detectors for reliable distributed systems. Journal of the ACM, 43(2):225-267, 1996.
Alejandro Cornejo, Nancy Lynch, Saira Viqar, and Jennifer L Welch. Neighbor Discovery in Mobile Ad Hoc Networks Using an Abstract MAC Layer. In Proceedings of the Annual Allerton Conference on Communication, Control, and Computing, 2009.
Alejandro Cornejo, Saira Viqar, and Jennifer L Welch. Reliable Neighbor Discovery for Mobile Ad Hoc Networks. Ad Hoc Networks, 12:259-277, 2014.
A. Czumaj and W. Rytter. Broadcasting Algorithms in Radio Networks with Unknown Topology. Journal of Algorithms, 60:115-143, 2006.
Sebastian Daum, Seth Gilbert, Fabian Kuhn, and Calvin Newport. Broadcast in the Ad Hoc SINR Model. In Proceedings of the International Conference on Distributed Computing, 2013.
Cynthia Dwork, David Peleg, Nicholas Pippenger, and Eli Upfal. Fault tolerance in networks of bounded degree. SIAM Journal on Computing, 17(5):975-988, 1988.
Michael J Fischer, Nancy A Lynch, and Michael S Paterson. Impossibility of distributed consensus with one faulty process. Journal of the ACM, 32(2), 1985.
L. Gasieniec, D. Peleg, and Q. Xin. Faster Communication in Known Topology Radio Networks. Distributed Computing, 19(4):289-300, 2007.
O. Goussevskaia, R. Wattenhofer, M.M. Halldorsson, and E. Welzl. Capacity of Arbitrary Wireless Networks. In Proceedings of the IEEE International Conference on Computer Communications, 2009.
Fabiola Greve and Sebastien Tixeuil. Knowledge connectivity vs. synchrony requirements for fault-tolerant agreement in unknown networks. In Proceedings of the IEEE/IFIP International Conference on Dependable Systems and Networks, 2007.
Rachid Guerraoui, Michel Hurfinn, Achour Mostéfaoui, Riucarlos Oliveira, Michel Raynal, and André Schiper. Consensus in asynchronous distributed systems: A concise guided tour. Advances in Distributed Systems, Lecture Notes in Computer Science, 1752:33-47, 2000.
Rachid Guerraoui and Andre Schiper. Consensus: the big misunderstanding [distributed fault tolerant systems]. In Proceedings of the IEEE Computer Society Workshop on Future Trends of Distributed Computing Systems, 1997.
Rachid Guerraoui and André Schiper. The generic consensus service. IEEE Transactions on Software Engineering, 27(1):29-41, 2001.
Magnus M. Halldorsson and Pradipta Mitra. Wireless Connectivity and Capacity. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2012.
Tomasz Jurdzinski, Dariusz R. Kowalski, Michal Rozanski, and Grzegorz Stachowiak. Distributed Randomized Broadcasting in Wireless Networks under the SINR Model. In Proceedings of the International Conference on Distributed Computing, 2013.
Tomasz Jurdziński and Grzegorz Stachowiak. Probabilistic Algorithms for the Wakeup Problem in Single-Hop Radio Networks. In Algorithms and Computation, pages 535-549. Springer, 2002.
Majid Khabbazian, Fabian Kuhn, Dariusz Kowalski, and Nancy Lynch. Decomposing Broadcast Algorithms Using Abstract MAC Layers. In Proceedings of the International Workshop on the Foundations of Mobile Computing, 2010.
Majid Khabbazian, Fabian Kuhn, Nancy Lynch, Muriel Medard, and Ali ParandehGheibi. MAC Design for Analog Network Coding. In Proceedings of the International Workshop on the Foundations of Mobile Computing, 2011.
Valerie King, Jared Saia, Vishal Sanwalani, and Erik Vee. Towards secure and scalable computation in peer-to-peer networks. In Foundations of Computer Science, 2006. FOCS'06. 47th Annual IEEE Symposium on, pages 87-98. IEEE, 2006.
D.R. Kowalski and A. Pelc. Broadcasting in Undirected Ad Hoc Radio Networks. Distributed Computing, 18(1):43-57, 2005.
Fabian Kuhn, Nancy Lynch, and Calvin Newport. The Abstract MAC Layer. In Proceedings of the International Conference on Distributed Computing, 2009.
Fabian Kuhn, Nancy Lynch, and Calvin Newport. The Abstract MAC Layer. Distributed Computing, 24(3-4):187-206, 2011.
Leslie Lamport. The part-time parliament. ACM Transactions on Computer Systems, 16(2):133-169, 1998.
Nancy A Lynch. Distributed algorithms. Morgan Kaufmann, 1996.
Thomas Moscibroda. The Worst-Case Capacity of Wireless Sensor Networks. In Proceedings of the ACM/IEEE International Conference on Information Processing in Sensor Networks, 2007.
Thomas Moscibroda and Roger Wattenhofer. Maximal Independent Sets in Radio Networks. In Proceedings of the ACM Conference on Distributed Computing, 2005.
Thomas Moscibroda and Roger Wattenhofer. The Complexity of Connectivity in Wireless Networks. In Proceedings of the IEEE International Conference on Computer Communications, 2006.
Achour Mostefaoui and Michel Raynal. Solving consensus using Chandra-Touegs unreliable failure detectors. Lecture Notes in Computer Science, 1693:49-63, 1999.
Calvin Newport. Consensus with an Abstract MAC Layer. In Proceedings of the ACM Conference on Distributed Computing, 2014.
Calvin Newport and Peter Robinson. Fault-Tolerant Consensus with an Abstract MAC Layer. Technical report, https://www.cas.mcmaster.ca/robinson/random-aml.pdf, 2018.
https://www.cas.mcmaster.ca/robinson/random-aml.pdf
Eric Ruppert. The Anonymous Consensus Hierarchy and Naming Problems. In Proceedings of the International Conference on Principles of Distributed Systems, 2007.
Andre Schiper. Early consensus in an asynchronous system with a weak failure detector. Distributed Computing, 10(3):149-157, 1997.
Einar W Vollset and Paul D Ezhilchelvan. Design and performance-study of crash-tolerant protocols for broadcasting and reaching consensus in MANETs. In IEEE Symposium on Reliable Distributed Systems, 2005.
Weigang Wu, Jiannong Cao, and Michel Raynal. Eventual clusterer: A modular approach to designing hierarchical consensus protocols in manets. IEEE Transactions onParallel and Distributed Systems, 20(6):753-765, 2009.
Calvin Newport and Peter Robinson
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Randomized (Delta+1)-Coloring in O(log* Delta) Congested Clique Rounds
(Delta+1)-vertex coloring is one of the most fundamental symmetry breaking graph problems, receiving tremendous amount of attention over the last decades. We consider the congested clique model where in each round, every pair of vertices can exchange O(log n) bits of information.
In a recent breakthrough, Yi-Jun Chang, Wenzheng Li, and Seth Pettie [CLP-STOC'18] presented a randomized (Delta+1)-list coloring algorithm in the LOCAL model that works in O(log^*n+Det_{deg}(log log n)) rounds, where Det_{deg}(n') is the deterministic LOCAL complexity of (deg+1)-list coloring algorithm on n'-vertex graphs. Unfortunately, the CLP algorithm uses large messages and hence cannot be efficiently implemented in the congested clique model when the maximum degree Delta is large (in particular, when Delta=omega(sqrt{n})).
Merav Parter [P-ICALP'18] recently provided a randomized (Delta+1)-coloring algorithm in O(log log Delta * log^* Delta) congested clique rounds based on a careful partitioning of the input graph into almost-independent subgraphs with maximum degree sqrt{n}. In this work, we significantly improve upon this result and present a randomized (Delta+1)-coloring algorithm with O(log^* Delta) rounds, with high probability. At the heart of our algorithm is an adaptation of the CLP algorithm for coloring a subgraph with o(n) vertices and maximum degree Omega(n^{5/8}) in O(log^* Delta) rounds. The approach is built upon a combination of techniques, this includes: the graph sparsification of [Parter-ICALP'18], and a palette sampling technique adopted to the CLP framework.
Distributed Graph Algorithms
Coloring
congested clique
Theory of computation~Distributed algorithms
39:1-39:18
Regular Paper
Merav
Parter
Merav Parter
Weizmann IS, Rehovot, Israel
Hsin-Hao
Su
Hsin-Hao Su
UNC-Charlotte, North Carolina, USA
10.4230/LIPIcs.DISC.2018.39
Leonid Barenboim and Victor Khazanov. Distributed symmetry-breaking algorithms for congested cliques. arXiv preprint arXiv:1802.07209, 2018.
Soheil Behnezhad, Mahsa Derakhshan, and MohammadTaghi Hajiaghayi. Brief announcement: Semi-mapreduce meets congested clique. arXiv preprint arXiv:1802.10297, 2018.
Andrew Berns, James Hegeman, and Sriram V Pemmaraju. Super-fast distributed algorithms for metric facility location. In International Colloquium on Automata, Languages, and Programming, pages 428-439. Springer, 2012.
Keren Censor-Hillel, Merav Parter, and Gregory Schwartzman. Derandomizing local distributed algorithms under bandwidth restrictions. In 31st International Symposium on Distributed Computing, DISC 2017, October 16-20, 2017, Vienna, Austria, pages 11:1-11:16, 2017.
Yi-Jun Chang, Wenzheng Li, and Seth Pettie. An optimal distributed (Δ+1)-coloring algorithm? In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, Los Angeles, CA, USA, pages 445-456. ACM, 2018.
Mohsen Ghaffari. Distributed MIS via all-to-all communication. In Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2017, Washington, DC, USA, July 25-27, 2017, pages 141-149, 2017.
Mohsen Ghaffari, Themis Gouleakis, Christian Konrad, Slobodan Mitrovic, and Ronitt Rubinfeld. Improved massively parallel computation algorithms for mis, matching, and vertex cover. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC 2018, Egham, United Kingdom, pages 129-138, 2018.
David G Harris, Johannes Schneider, and Hsin-Hao Su. Distributed (Δ+ 1)-coloring in sublogarithmic rounds. In Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, pages 465-478. ACM, 2016.
James W Hegeman and Sriram V Pemmaraju. Lessons from the congested clique applied to mapreduce. Theoretical Computer Science, 608:268-281, 2015.
James W Hegeman, Sriram V Pemmaraju, and Vivek B Sardeshmukh. Near-constant-time distributed algorithms on a congested clique. In International Symposium on Distributed Computing, pages 514-530. Springer, 2014.
Tomasz Jurdzinski and Krzysztof Nowicki. MST in O(1) rounds of congested clique. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, January 7-10, 2018, pages 2620-2632, 2018.
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. Local computation: Lower and upper bounds. Journal of the ACM (JACM), 63(2):17, 2016.
Christoph Lenzen. Optimal deterministic routing and sorting on the congested clique. In Proceedings of the 2013 ACM symposium on Principles of distributed computing, pages 42-50. ACM, 2013.
Zvi Lotker, Boaz Patt-Shamir, Elan Pavlov, and David Peleg. Minimum-weight spanning tree construction in O (log log n) communication rounds. SIAM Journal on Computing, 35(1):120-131, 2005.
Merav Parter. (Δ+1) coloring in the congested clique model. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018), volume 107 of Leibniz International Proceedings in Informatics (LIPIcs), pages 160:1-160:14. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018.
Merav Parter. (Δ+1) coloring in the congested clique model. arXiv preprint, 2018. URL: http://arxiv.org/abs/1805.02457.
http://arxiv.org/abs/1805.02457
Johannes Schneider and Roger Wattenhofer. A new technique for distributed symmetry breaking. In Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pages 257-266. ACM, 2010.
Merav Parter and Hsin-Hao Su
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Congested Clique Algorithms for Graph Spanners
Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling schemes and routing to solving linear systems and spectral sparsification. A k-spanner maintains pairwise distances up to multiplicative factor of k. It is a folklore that for every n-vertex graph G, one can construct a (2k-1) spanner with O(n^{1+1/k}) edges. In a distributed setting, such spanners can be constructed in the standard CONGEST model using O(k^2) rounds, when randomization is allowed.
In this work, we consider spanner constructions in the congested clique model, and show:
- a randomized construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k) rounds. The previous best algorithm runs in O(k) rounds;
- a deterministic construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k +(log log n)^3) rounds. The previous best algorithm runs in O(k log n) rounds. This improvement is achieved by a new derandomization theorem for hitting sets which might be of independent interest;
- a deterministic construction of a O(k)-spanner with O(k * n^{1+1/k}) edges in O(log k) rounds.
Distributed Graph Algorithms
Spanner
Congested Clique
Theory of computation~Distributed algorithms
40:1-40:18
Regular Paper
https://arxiv.org/abs/1805.05404
Merav
Parter
Merav Parter
Weizmann IS, Rehovot, Israel
Eylon
Yogev
Eylon Yogev
Weizmann IS, Rehovot, Israel
10.4230/LIPIcs.DISC.2018.40
Leonid Barenboim and Victor Khazanov. Distributed symmetry-breaking algorithms for congested cliques. arXiv preprint arXiv:1802.07209, 2018.
Surender Baswana and Sandeep Sen. A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs. Random Structures and Algorithms, 30(4):532-563, 2007.
Ruben Becker, Andreas Karrenbauer, Sebastian Krinninger, and Christoph Lenzen. Near-optimal approximate shortest paths and transshipment in distributed and streaming models. In DISC, 2017.
Soheil Behnezhad, Mahsa Derakhshan, and MohammadTaghi Hajiaghayi. Brief announcement: Semi-mapreduce meets congested clique. arXiv preprint arXiv:1802.10297, 2018.
Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, and David P Woodruff. Transitive-closure spanners. SIAM Journal on Computing, 41(6):1380-1425, 2012.
L Elisa Celis, Omer Reingold, Gil Segev, and Udi Wieder. Balls and bins: Smaller hash families and faster evaluation. SIAM Journal on Computing, 42(3):1030-1050, 2013.
Keren Censor-Hillel, Merav Parter, and Gregory Schwartzman. Derandomizing local distributed algorithms under bandwidth restrictions. In 31 International Symposium on Distributed Computing, 2017.
Bilel Derbel and Cyril Gavoille. Fast deterministic distributed algorithms for sparse spanners. Theoretical Computer Science, 2008.
Bilel Derbel, Cyril Gavoille, and David Peleg. Deterministic distributed construction of linear stretch spanners in polylogarithmic time. In DISC, pages 179-192. Springer, 2007.
Bilel Derbel, Cyril Gavoille, David Peleg, and Laurent Viennot. On the locality of distributed sparse spanner construction. In PODC, pages 273-282, 2008.
Bilel Derbel, Cyril Gavoille, David Peleg, and Laurent Viennot. Local computation of nearly additive spanners. In DISC, 2009.
Bilel Derbel, Mohamed Mosbah, and Akka Zemmari. Sublinear fully distributed partition with applications. Theory of Computing Systems, 47(2):368-404, 2010.
Mohsen Ghaffari. An improved distributed algorithm for maximal independent set. Manuescript, 2018.
Mohsen Ghaffari, Themis Gouleakis, Slobodan Mitrović, and Ronitt Rubinfeld. Improved massively parallel computation algorithms for mis, matching, and vertex cover. PODC, 2018.
Parikshit Gopalan, Raghu Meka, Omer Reingold, Luca Trevisan, and Salil P. Vadhan. Better pseudorandom generators from milder pseudorandom restrictions. In 53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012, New Brunswick, NJ, USA, October 20-23, 2012, pages 120-129, 2012.
Ofer Grossman and Merav Parter. Improved deterministic distributed construction of spanners. In DISC, 2017.
James W Hegeman and Sriram V Pemmaraju. Lessons from the congested clique applied to mapreduce. Theoretical Computer Science, 608:268-281, 2015.
Christoph Lenzen. Optimal deterministic routing and sorting on the congested clique. In the Proc. of the Int'l Symp. on Princ. of Dist. Comp. (PODC), pages 42-50, 2013.
Christoph Lenzen and Roger Wattenhofer. Brief announcement: exponential speed-up of local algorithms using non-local communication. In Proceedings of the 29th Annual ACM Symposium on Principles of Distributed Computing, PODC 2010, Zurich, Switzerland, July 25-28, 2010, pages 295-296, 2010.
Zvi Lotker, Elan Pavlov, Boaz Patt-Shamir, and David Peleg. MST construction in O(log log n) communication rounds. In the Proceedings of the Symposium on Parallel Algorithms and Architectures, pages 94-100. ACM, 2003.
Merav Parter and Eylon Yogev. Congested clique algorithms for graph spanners. arXiv preprint, 2018. URL: http://arxiv.org/abs/1805.05404.
http://arxiv.org/abs/1805.05404
David Peleg. Distributed Computing: A Locality-sensitive Approach. SIAM, 2000.
David Peleg and Alejandro A Schäffer. Graph spanners. Journal of graph theory, 13(1):99-116, 1989.
David Peleg and Jeffrey D Ullman. An optimal synchronizer for the hypercube. SIAM Journal on computing, 18(4):740-747, 1989.
Seth Pettie. Distributed algorithms for ultrasparse spanners and linear size skeletons. Distributed Computing, 22(3):147-166, 2010.
Liam Roditty, Mikkel Thorup, and Uri Zwick. Deterministic constructions of approximate distance oracles and spanners. In International Colloquium on Automata, Languages, and Programming, pages 261-272. Springer, 2005.
Mikkel Thorup and Uri Zwick. Compact routing schemes. In Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures, pages 1-10. ACM, 2001.
Virginia Vassilevska Williams. Graph algorithms - Fall 2016, MIT, lecture notes 5, 2016. URL: http://theory.stanford.edu/~virgi/cs267/lecture5.pdf.
http://theory.stanford.edu/~virgi/cs267/lecture5.pdf
Merav Parter and Eylon Yogev
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Lattice Agreement in Message Passing Systems
This paper studies the lattice agreement problem and the generalized lattice agreement problem in distributed message passing systems. In the lattice agreement problem, given input values from a lattice, processes have to non-trivially decide output values that lie on a chain. We consider the lattice agreement problem in both synchronous and asynchronous systems. For synchronous lattice agreement, we present two algorithms which run in log(f) and min{O(log^2 h(L)), O(log^2 f)} rounds, respectively, where h(L) denotes the height of the input sublattice L, f < n is the number of crash failures the system can tolerate, and n is the number of processes in the system. These algorithms have significant better round complexity than previously known algorithms. The algorithm by Attiya et al. [Attiya et al. DISC, 1995] takes log(n) synchronous rounds, and the algorithm by Mavronicolasa [Mavronicolasa, 2018] takes min{O(h(L)), O(sqrt(f))} rounds. For asynchronous lattice agreement, we propose an algorithm which has time complexity of 2*min{h(L), f + 1} message delays which improves on the previously known time complexity of O(n) message delays.
The generalized lattice agreement problem defined by Faleiro et al in [Faleiro et al. PODC, 2012] is a generalization of the lattice agreement problem where it is applied for the replicated state machine. We propose an algorithm which guarantees liveness when a majority of the processes are correct in asynchronous systems. Our algorithm requires min{O(h(L)), O(f)} units of time in the worst case which is better than O(n) units of time required by the algorithm in [Faleiro et al. PODC, 2012].
Lattice Agreement
Replicated State Machine
Consensus
Theory of computation~Distributed algorithms
41:1-41:17
Regular Paper
Supported by NSF CNS-1812349, NSF CNS-1563544, NSF CNS-1346245, Huawei Inc., and the Cullen Trust for Higher Education Endowed Professorship.
https://arxiv.org/abs/1807.11557
Xiong
Zheng
Xiong Zheng
University of Texas at Austin, Austin, TX 78712, USA
Changyong
Hu
Changyong Hu
University of Texas at Austin, Austin, TX 78712, USA
Vijay K.
Garg
Vijay K. Garg
University of Texas at Austin, Austin, TX 78712, USA
10.4230/LIPIcs.DISC.2018.41
Yehuda Afek, Hagit Attiya, Danny Dolev, Eli Gafni, Michael Merritt, and Nir Shavit. Atomic snapshots of shared memory. Journal of the ACM (JACM), 40(4):873-890, 1993.
Hagit Attiya, Maurice Herlihy, and Ophir Rachman. Atomic snapshots using lattice agreement. Distributed Computing, 8(3):121-132, 1995.
Hagit Attiya and Ophir Rachman. Atomic snapshots in 𝒪 (n log n) operations. SIAM Journal on Computing, 27(2):319-340, 1998.
Hagit Attiya and Jennifer Welch. Distributed computing: fundamentals, simulations, and advanced topics, volume 19. John Wiley &Sons, 2004.
Carole Delporte-Gallet, Hugues Fauconnier, Sergio Rajsbaum, and Michel Raynal. Implementing snapshot objects on top of crash-prone asynchronous message-passing systems. In International Conference on Algorithms and Architectures for Parallel Processing, pages 341-355. Springer, 2016.
Danny Dolev and H Raymond Strong. Authenticated algorithms for byzantine agreement. SIAM Journal on Computing, 12(4):656-666, 1983.
Jose M Faleiro, Sriram Rajamani, Kaushik Rajan, G Ramalingam, and Kapil Vaswani. Generalized lattice agreement. In Proceedings of the 2012 ACM symposium on Principles of distributed computing, pages 125-134. ACM, 2012.
Michael J Fischer, Nancy A Lynch, and Michael S Paterson. Impossibility of distributed consensus with one faulty process. Journal of the ACM (JACM), 32(2):374-382, 1985.
Maurice P Herlihy and Jeannette M Wing. Linearizability: A correctness condition for concurrent objects. ACM Transactions on Programming Languages and Systems (TOPLAS), 12(3):463-492, 1990.
Leslie Lamport. The part-time parliament. ACM Transactions on Computer Systems (TOCS), 16(2):133-169, 1998.
Leslie Lamport et al. Paxos made simple. ACM Sigact News, 32(4):18-25, 2001.
Marios Mavronicolas. A bound on the rounds to reach lattice agreement, 2000. URL: http://www.cs.ucy.ac.cy/~mavronic/pdf/lattice.pdf.
http://www.cs.ucy.ac.cy/~mavronic/pdf/lattice.pdf
Michel Raynal. Concurrent programming: algorithms, principles, and foundations. Springer Science &Business Media, 2012.
Fred B Schneider. Implementing fault-tolerant services using the state machine approach: A tutorial. ACM Computing Surveys (CSUR), 22(4):299-319, 1990.
Marc Shapiro, Nuno Preguiça, Carlos Baquero, and Marek Zawirski. Conflict-free replicated data types. In Symposium on Self-Stabilizing Systems, pages 386-400. Springer, 2011.
Marc Shapiro, Nuno Preguiça, Carlos Baquero, and Marek Zawirski. Convergent and commutative replicated data types. Bulletin-European Association for Theoretical Computer Science, 104:67-88, 2011.
Andrew S Tanenbaum and Maarten Van Steen. Distributed systems: principles and paradigms. Prentice-Hall, 2007.
Gadi Taubenfeld. Synchronization algorithms and concurrent programming. Pearson Education, 2006.
Xiong Zheng, Changyong Hu, and Vijay K. Garg
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: Local Distributed Algorithms in Highly Dynamic Networks
We define a generalization of local distributed graph problems to (synchronous round-based) dynamic networks and present a framework for developing algorithms for these problems. We require two properties from our algorithms: (1) They should satisfy non-trivial guarantees in every round. The guarantees should be stronger the more stable the graph has been during the last few rounds and they coincide with the definition of the static graph problem if no topological change appeared recently. (2) If a constant neighborhood around some part of the graph is stable during an interval, the algorithms quickly converge to a solution for this part of the graph that remains unchanged throughout the interval.
We demonstrate our generic framework with two classic distributed graph, namely (degree+1)-vertex coloring and maximal independent set (MIS).
dynamic networks
distributed graph algorithms
MIS
vertex coloring
Networks~Network algorithms
42:1-42:4
Brief Announcement
Second and third author were supported by ERC Grant No. 336495 (ACDC).
Philipp
Bamberger
Philipp Bamberger
University of Freiburg, Georges-Köhler-Allee 106, 79110 Freiburg, Germany
Fabian
Kuhn
Fabian Kuhn
University of Freiburg, Georges-Köhler-Allee 106, 79110 Freiburg, Germany
Yannic
Maus
Yannic Maus
University of Freiburg, Georges-Köhler-Allee 106, 79110 Freiburg, Germany
10.4230/LIPIcs.DISC.2018.42
N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. of Algorithms, 7(4):567-583, 1986.
S. Assadi, K. Onak, B. Schieber, and S. Solomon. Fully dynamic maximal independent set with sublinear update time. In Proc. 50th ACM Symp. on Theory of Comp. (STOC), 2018.
K. Censor-Hillel, E. Haramaty, and Z.S. Karnin. Optimal dynamic distributed MIS. In Proc. 35th ACM Symp. on Principles of Distr. Computing (PODC), pages 217-226, 2016.
P. Fraigniaud, A. Korman, and D. Peleg. Local distributed decision. In Proc. 52nd Symp. on Foundations of Computer Sc. (FOCS), pages 708-717. IEEE Computer Society, 2011.
M. Ghaffari. An improved distributed algorithm for maximal independent set. In Proc. 27th ACM-SIAM Symp. on Discrete Algorithms (SODA), pages 270-277, 2016.
M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Comp., 15:1036-1053, 1986.
Philipp Bamberger, Fabian Kuhn, and Yannic Maus
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: Randomized Blind Radio Networks
Radio networks are a long-studied model for distributed system of devices which communicate wirelessly. When these devices are mobile or have limited capabilities, the system is best modeled by the ad-hoc variant, in which the devices do not know the structure of the network. Much work has been devoted to designing algorithms for the ad-hoc model, particularly for fundamental communications tasks such as broadcasting. Most of these algorithms, however, assume that devices have some network knowledge (usually bounds on the number of nodes in the network n, and the diameter D), which may not be realistic in systems with weak devices or gradual deployment. Little is known about what can be done without this information.
This is the issue we address in this work, by presenting the first randomized broadcasting algorithms for blind networks in which nodes have no prior knowledge whatsoever. We demonstrate that lack of parameter knowledge can be overcome at only a small increase in running time. Specifically, we show that in networks without collision detection, broadcast can be achieved in O(D log n/D log^2 log n/D + log^2 n) time, almost reaching the Omega(D log n/D + log^2 n) lower bound. We also give an even faster algorithm for directed networks with collision detection.
Broadcasting
Randomized Algorithms
Radio Networks
Theory of computation~Distributed algorithms
Networks~Network algorithms
43:1-43:3
Brief Announcement
Research partially supported by the Centre for Discrete Mathematics and its Applications (DIMAP), by EPSRC award EP/D063191/1, and by EPSRC award EP/N011163/1.
Artur
Czumaj
Artur Czumaj
University of Warwick, Coventry, UK
Peter
Davies
Peter Davies
University of Warwick, Coventry, UK
10.4230/LIPIcs.DISC.2018.43
N. Alon, A. Bar-Noy, N. Linial, and D. Peleg. A lower bound for radio broadcast. Journal of Computer and System Sciences, 43(2):290-298, 1991.
A. Czumaj and P. Davies. Communicating with beeps. In Proceedings of the 19th International Conference on Principles of Distributed Systems (OPODIS), pages 1-16, 2015.
A. Czumaj and W. Rytter. Broadcasting algorithms in radio networks with unknown topology. In Proceedings of the 44th IEEE Symposium on Foundations of Computer Science (FOCS), pages 492-501, 2003.
T. Jurdziński and G. Stachowiak. Probabilistic algorithms for the wakeup problem in single-hop radio networks. Theory of Computing Systems, 38(3):347-367, 2005.
D. Kowalski and A. Pelc. Broadcasting in undirected ad hoc radio networks. Distributed Computing, 18(1):43-57, 2005.
E. Kushilevitz and Y. Mansour. An Ω(D log(N/D)) lower bound for broadcast in radio networks. SIAM Journal on Computing, 27(3):702-712, 1998.
Artur Czumaj and Peter Davies
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: Deterministic Contention Resolution on a Shared Channel
A shared channel, also called multiple-access channel, is one of the fundamental communication models. Autonomous entities communicate over a shared medium, and one of the main challenges is how to efficiently resolve collisions occurring when more than one entity attempts to access the channel at the same time. In this work we explore the impact of asynchrony, knowledge (or linear estimate) of the number of contenders, and acknowledgments, on both latency and channel utilization for the Contention resolution problem with non-adaptive deterministic algorithms.
Shared channel
multiple-access channel
distributed algorithm
Theory of computation~Distributed algorithms
44:1-44:3
Brief Announcement
Gianluca
De Marco
Gianluca De Marco
Dipartimento di Informatica, University of Salerno, Italy
Dariusz R.
Kowalski
Dariusz R. Kowalski
Department of Computer Science, University of Liverpool, UK
Grzegorz
Stachowiak
Grzegorz Stachowiak
Institute of Computer Science, University Wrocław, Poland
10.4230/LIPIcs.DISC.2018.44
A. Fernández Anta, M. A. Mosteiro, and J. Ramon Mu noz. Unbounded contention resolution in multiple-access channels. Algorithmica, 67:295-314, 2013.
M. A. Bender, M. Farach-Colton, S. He, B. C. Kuszmaul, and C. E. Leiserson. Adversarial contention resolution for simple channels. In Proceedings, 17th ACM Symp. on Parallel Algorithms (SPAA), pages 325-332, New York, NY, USA, 2005. ACM.
M. A. Bender, T. Kopelowitz, S. Pettie, and M. Young. Contention resolution with log-logstar channel accesses. In Proceedings, 48th ACM Symp. on Theory of Computing (STOC), pages 499-508, Cambridge, MA, USA, 2016. ACM.
B. S. Chlebus. Randomized communication in radio networks. In P. M. Pardalos, S. Rajasekaran, J. H. Reif, and J. D. P. Rolim, editors, Handbook on Randomized Computing, pages 401-456. Springer, New York, NY, USA, 2001.
B. S. Chlebus, G. De Marco, and D. R. Kowalski. Scalable wake-up of multi-channel single-hop radio networks. Theor. Comput. Sci., 615:23-44, 2016. URL: http://dx.doi.org/10.1016/j.tcs.2015.11.046.
http://dx.doi.org/10.1016/j.tcs.2015.11.046
B. S. Chlebus, D. R. Kowalski, and M. A. Rokicki. Adversarial queuing on the multiple access channel. ACM Trans. on Algorithms, 8:5:1-5:31, 2012.
G. De Marco and D. R. Kowalski. Contention resolution in a non-synchronized multiple access channel. Theor. Comput. Sci., 689:1-13, 2017. URL: http://dx.doi.org/10.1016/j.tcs.2017.05.014.
http://dx.doi.org/10.1016/j.tcs.2017.05.014
G. De Marco and G. Stachowiak. Asynchronous shared channel. In Proceedings, ACM Symp. on Principles of Distributed Computing, PODC 2017, Washington, DC, USA, July 25-27, 2017, pages 391-400, 2017. URL: http://dx.doi.org/10.1145/3087801.3087831.
http://dx.doi.org/10.1145/3087801.3087831
Robert G. Gallager. A perspective on multiaccess channels. IEEE Trans. Information Theory, 31(2):124-142, 1985.
L. A. Goldberg, P. D. MacKenzie, M. Paterson, and A. Srinivasan. Contention resolution with constant expected delay. J. ACM, 47(6):1048-1096, 2000.
A. G. Greenberg and A S. Winograd. Lower bound on the time needed in the worst case to resolve conflicts deterministically in multiple access channels. J. ACM, 32:589-596, 1985.
J. Komlós and A. G. Greenberg. An asymptotically optimal nonadaptive algorithm for conflict resolution in multiple-access channels. IEEE Trans. on Information Theory, 31:302-306, 1985.
D. Kowalski. On selection problem in radio networks. In Proceedings, 24th ACM Symp. on Principles of Distributed Computing (PODC), pages 158-166, Las Vegas, NV, USA, 2005. ACM.
Gianluca De Marco, Dariusz R. Kowalski, and Grzegorz Stachowiak
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: Generalising Concurrent Correctness to Weak Memory
Correctness conditions like linearizability and opacity describe some form of atomicity imposed on concurrent objects. In this paper, we propose a correctness condition (called causal atomicity) for concurrent objects executing in a weak memory model, where the histories of the objects in question are partially ordered. We establish compositionality and abstraction results for causal atomicity and develop an associated refinement-based proof technique.
Weak Memory
Concurrent Object
Execution Structure
Theory of computation~Concurrency
Theory of computation~Shared memory algorithms
45:1-45:3
Brief Announcement
Simon
Doherty
Simon Doherty
Department of Computer Science, University of Sheffield, UK
Simon Doherty and John Derrick are funded by EPSRC Grant EP/M017044/1.
Brijesh
Dongol
Brijesh Dongol
Department of Computer Science, University of Surrey, Guildford, UK
Funded by EPSRC Grant EP/R019045/1.
Heike
Wehrheim
Heike Wehrheim
Department of Computer Science, Paderborn University, Paderborn, Germany
John
Derrick
John Derrick
Department of Computer Science, University of Sheffield, UK
10.4230/LIPIcs.DISC.2018.45
S. Doherty, B. Dongol, H. Wehrheim, and J. Derrick. Making Linearizability Compositional for Partially Ordered Executions. In iFM, volume 11023 of LNCS, 2018.
S. Doherty, L. Groves, V. Luchangco, and M. Moir. Towards formally specifying and verifying transactional memory. Formal Asp. Comput., 25(5):769-799, 2013.
A. Farzan and P. Madhusudan. Causal atomicity. In CAV, volume 4144 of LNCS, pages 315-328. Springer, 2006.
L. Lamport. On interprocess communication. part I: basic formalism. Distributed Computing, 1(2):77-85, 1986.
Simon Doherty, Brijesh Dongol, Heike Wehrheim, and John Derrick
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: Exact Size Counting in Uniform Population Protocols in Nearly Logarithmic Time
We study population protocols: networks of anonymous agents whose pairwise interactions are chosen uniformly at random. The size counting problem is that of calculating the exact number n of agents in the population, assuming no leader (each agent starts in the same state). We give the first protocol that solves this problem in sublinear time.
The protocol converges in O(log n log log n) time and uses O(n^60) states (O(1) + 60 log n bits of memory per agent) with probability 1-O((log log n)/n). The time to converge is also O(log n log log n) in expectation. Crucially, unlike most published protocols with omega(1) states, our protocol is uniform: it uses the same transition algorithm for any population size, so does not need an estimate of the population size to be embedded into the algorithm.
population protocol
counting
leader election
polylogarithmic time
Theory of computation~Distributed algorithms
46:1-46:3
Brief Announcement
DD, ME: NSF grant CCF-1619343. OM, PS, MT: EEE/CS initiative NeST. MT: Leverhulme Research Centre for Functional Materials Design.
David
Doty
David Doty
Department of Computer Science, University of California, Davis
Mahsa
Eftekhari
Mahsa Eftekhari
Department of Computer Science, University of California, Davis
Othon
Michail
Othon Michail
Department of Computer Science, University of Liverpool, UK
Paul G.
Spirakis
Paul G. Spirakis
Department of Computer Science, University of Liverpool, UK and Computer Technology Institute & Press "Diophantus" (CTI), Patras, Greece
Michail
Theofilatos
Michail Theofilatos
Department of Computer Science, University of Liverpool, UK
10.4230/LIPIcs.DISC.2018.46
Dan Alistarh, James Aspnes, David Eisenstat, Rati Gelashvili, and Ronald L Rivest. Time-space trade-offs in population protocols. In SODA, 2017.
Dan Alistarh, James Aspnes, and Rati Gelashvili. Space-optimal majority in population protocols. In SODA, 2018.
Dan Alistarh and Rati Gelashvili. Polylogarithmic-time leader election in population protocols. In ICALP, 2015.
Dana Angluin, James Aspnes, Zoë Diamadi, Michael J. Fischer, and René Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Computing, 18(4):235-253, 2006.
Dana Angluin, James Aspnes, and David Eisenstat. Stably computable predicates are semilinear. In PODC, 2006.
Dana Angluin, James Aspnes, and David Eisenstat. Fast computation by population protocols with a leader. Distributed Computing, 21(3):183-199, 2008.
Petra Berenbrink, Dominik Kaaser, Peter Kling, and Lena Otterbach. Simple and Efficient Leader Election. In SOSA, 2018.
Andreas Bilke, Colin Cooper, Robert Elsässer, and Tomasz Radzik. Brief announcement: Population protocols for leader election and exact majority with O(log² n) states and O(log² n) convergence time. In PODC, 2017.
Leszek Gasieniec and Grzegorz Stachowiak. Fast space optimal leader election in population protocols. In SODA, 2018.
Yves Mocquard, Emmanuelle Anceaume, James Aspnes, Yann Busnel, and Bruno Sericola. Counting with population protocols. In NCA, 2015.
David Doty, Mahsa Eftekhari, Othon Michail, Paul G. Spirakis, and Michail Theofilatos
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: A Tight Lower Bound for Clock Synchronization in Odd-Ary M-Toroids
In this paper we show a tight closed-form expression for the optimal clock synchronization in k-ary m-cubes with wraparound, where k is odd. This is done by proving a lower bound of 1/4um (k-1/k), where k is the (odd) number of processes in each of the m dimensions, and u is the uncertainty in delay on every link. Our lower bound matches the previously known upper bound.
Clock synchronization
Lower bound
k-ary m-toroid
Theory of computation~Distributed algorithms
47:1-47:3
Brief Announcement
https://arxiv.org/abs/1807.05139
Reginald
Frank
Reginald Frank
Texas A&M University, College Station, TX, USA
https://orcid.org/0000-0002-0423-1071
Supported in part by CRA-W and CDC’s DREU program and NSF grant CNS-0540631.
Jennifer L.
Welch
Jennifer L. Welch
Texas A&M University, College Station, TX, USA
Supported in part by NSF grant 1526725.
10.4230/LIPIcs.DISC.2018.47
Hagit Attiya, Amir Herzberg, and Sergio Rajsbaum. Optimal clock synchronization under different delay assumptions. SIAM J. Comput., 25(2):369-389, 1996.
Hagit Attiya and Jennifer L. Welch. Distributed Computing: Fundamentals, Simulations, and Advanced Topics, Second Edition. John Wiley &Sons, Hoboken, NJ, 2004.
Saad Biaz and Jennifer L. Welch. Closed form bounds for clock synchronization under simple uncertainty assumptions. Inf. Process. Lett., 80(3):151-157, 2001.
Joseph Y. Halpern, Nimrod Megiddo, and Ashfaq A. Munshi. Optimal precision in the presence of uncertainty. J. Complexity, 1(2):170-196, 1985.
Jennifer Lundelius and Nancy Lynch. An upper and lower bound for clock synchronization. Inform. Control, 62(2/3):190-204, 1984.
Boaz Patt-Shamir and Sergio Rajsbaum. A theory of clock synchronization (extended abstract). In Proc. 26th Annual ACM Symp. Theory of Comput., pages 810-819, 1994.
Reginald Frank and Jennifer L. Welch
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: On Simple Back-Off in Unreliable Radio Networks
In this paper, we study local broadcast in the dual graph model, which describes communication in a radio network with both reliable and unreliable links. Existing work proved that efficient solutions to these problems are impossible in the dual graph model under standard assumptions. In real networks, however, simple back-off strategies tend to perform well for solving these basic communication tasks. We address this apparent paradox by introducing a new set of constraints to the dual graph model that better generalize the slow/fast fading behavior common in real networks. We prove that in the context of these new constraints, simple back-off strategies now provide efficient solutions to local broadcast in the dual graph model. These results provide theoretical foundations for the practical observation that simple back-off algorithms tend to work well even amid the complicated link dynamics of real radio networks.
radio networks
broadcast
unreliable links
distributed algorithm
robustness
Theory of computation~Distributed algorithms
Networks~Ad hoc networks
48:1-48:3
Brief Announcement
https://arxiv.org/abs/1803.02216
Seth
Gilbert
Seth Gilbert
National University of Singapore
Nancy
Lynch
Nancy Lynch
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Calvin
Newport
Calvin Newport
Georgetown University, Washington, D.C., USA
Dominik
Pajak
Dominik Pajak
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
10.4230/LIPIcs.DISC.2018.48
Reuven Bar-Yehuda, Oded Goldreich, and Alon Itai. On the time-complexity of broadcast in multi-hop radio networks: An exponential gap between determinism and randomization. J. Comput. Syst. Sci., 45(1):104-126, 1992.
Mohsen Ghaffari, Bernhard Haeupler, Nancy A. Lynch, and Calvin C. Newport. Bounds on contention management in radio networks. In Distributed Computing - 26th International Symposium, DISC 2012, Salvador, Brazil, October 16-18, 2012. Proceedings, pages 223-237, 2012.
Mohsen Ghaffari, Nancy A. Lynch, and Calvin C. Newport. The cost of radio network broadcast for different models of unreliable links. In ACM Symposium on Principles of Distributed Computing, PODC '13, Montreal, QC, Canada, pages 345-354, 2013.
Seth Gilbert, Nancy Lynch, Calvin Newport, and Dominik Pajak
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: Fast and Scalable Group Mutual Exclusion
The group mutual exclusion (GME) problem is a generalization of the classical mutual exclusion problem in which every critical section is associated with a type or session. Critical sections belonging to the same session can execute concurrently, whereas critical sections belonging to different sessions must be executed serially. The well-known read-write mutual exclusion problem is a special case of the group mutual exclusion problem.
In a shared memory system, locks based on traditional mutual exclusion or its variants are commonly used to manage contention among processes. In concurrent algorithms based on fine-grained synchronization, a single lock is used to protect access to a small number of shared objects (e.g., a lock for every tree node) so as to minimize contention window. Evidently, a large number of shared objects in the system would translate into a large number of locks. Also, when fine-grained synchronization is used, most lock accesses are expected to be uncontended in practice.
Most existing algorithms for the solving the GME problem have high space-complexity per lock. Further, all algorithms except for one have high step-complexity in the uncontented case. This makes them unsuitable for use in concurrent algorithms based on fine-grained synchronization. In this work, we present a novel GME algorithm for an asynchronous shared-memory system that has O(1) space-complexity per GME lock when the system contains a large number of GME locks as well as O(1) step-complexity when the system contains no conflicting requests.
Group Mutual Exclusion
Fine-Grained Synchronization
Space Complexity
Contention-Free Step Complexity
Theory of computation~Concurrent algorithms
49:1-49:3
Brief Announcement
This work was supported, in part, by the National Science Foundation (NSF) under grants numbered CNS-1115733 and CNS-1619197.
Shreyas
Gokhale
Shreyas Gokhale
The University of Texas at Dallas , Richardson, TX 75080, USA
https://orcid.org/0000-0002-7589-6927
Neeraj
Mittal
Neeraj Mittal
The University of Texas at Dallas , Richardson, TX 75080, USA
https://orcid.org/0000-0002-8734-1400
10.4230/LIPIcs.DISC.2018.49
V. Bhatt and C. C. Huang. Group Mutual Exclusion in O(log n) RMR. In Proceedings of the 29th ACM Symposium on Principles of Distributed Computing (PODC), pages 45-54, JUL 2010.
R. Danek and V. Hadzilacos. Local-Spin Group Mutual Exclusion Algorithms. In Proceedings of the 18th Symposium on Distributed Computing (DISC), pages 71-85, OCT 2004.
S. Gokhale and N. Mittal. Fast and Scalable Group Mutual Exclusion. Available at http://arxiv.org/abs/1805.04819.
Y. He, K. Gopalakrishnan, and E. Gafni. Group Mutual Exclusion in Linear Time and Space. In Proceedings of the 17th International Conference on Distributed Computing And Networking (ICDCN), JAN 2016.
M. Herlihy and N. Shavit. The Art of Multiprocessor Programming, Revised Reprint. Morgan Kaufmann, 2012.
P. Jayanti, S. Petrovic, and K. Tan. Fair Group Mutual Exclusion. In Proceedings of the 22nd ACM Symposium on Principles of Distributed Computing (PODC), pages 275-284, JUL 2003.
Y.-J. Joung. Asynchronous Group Mutual Exclusion. Distributed Computing (DC), 13(4):189-206, 2000.
K. Platz. Saturation in Lock-Based Concurrent Data Structures. PhD thesis, Department of Computer Science, The University of Texas at Dallas, 2017.
Shreyas Gokhale and Neeraj Mittal
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: On the Impossibility of Detecting Concurrency
We identify a general principle of distributed computing: one cannot force two processes running in parallel to see each other. This principle is formally stated in the context of asynchronous processes communicating through shared objects, using trace-based semantics. We prove that it holds in a reasonable computational model, and then study the class of concurrent specifications which satisfy this property. This allows us to derive a Galois connection theorem for different variants of linearizability.
concurrent specification
concurrent object
linearizability
Theory of computation~Concurrency
50:1-50:4
Brief Announcement
Éric
Goubault
Éric Goubault
École Polytechnique, Palaiseau, France
Jérémy
Ledent
Jérémy Ledent
École Polytechnique, Palaiseau, France
Samuel
Mimram
Samuel Mimram
École Polytechnique, Palaiseau, France
10.4230/LIPIcs.DISC.2018.50
Armando Castañeda, Sergio Rajsbaum, and Michel Raynal. Specifying Concurrent Problems: Beyond Linearizability and up to Tasks. In DISC 2015, Proceedings, pages 420-435, 2015.
Nir Hemed, Noam Rinetzky, and Viktor Vafeiadis. Modular Verification of Concurrency-Aware Linearizability. In DISC 2015, Proceedings, pages 371-387, 2015.
Maurice Herlihy, Dmitry Kozlov, and Sergio Rajsbaum. Distributed Computing Through Combinatorial Topology. Morgan Kaufmann Publishers Inc., 2013.
Maurice Herlihy and Jeannette M. Wing. Linearizability: A Correctness Condition for Concurrent Objects. ACM Transactions on Programming Languages and Systems, 12(3):463-492, 1990.
L. Lamport. How to make a multiprocessor computer that correctly executes multiprocess programs. IEEE Transactions on Computers, 28(9):690-691, 1979.
Leslie Lamport. On interprocess communication. Distributed Computing, 1(2):77-85, 1986.
Richard J Lipton. Reduction: A method of proving properties of parallel programs. Communications of the ACM, 18(12):717-721, 1975.
J. Misra. Axioms for memory access in asynchronous hardware systems. In Stephen D. Brookes, Andrew William Roscoe, and Glynn Winskel, editors, Seminar on Concurrency, pages 96-110. Springer Berlin Heidelberg, 1985.
Gil Neiger. Set-Linearizability. In Proceedings of the Thirteenth Annual ACM Symposium on Principles of Distributed Computing, page 396, 1994.
Christos H. Papadimitriou. The serializability of concurrent database updates. Journal of the ACM, 26(4):631-653, 1979.
M. Raynal, G. Thia-Kime, and M. Ahamad. From serializable to causal transactions for collaborative applications. In Proceedings of the 23rd EUROMICRO, pages 314-321, 1997.
Éric Goubault and Jérémy Ledent and Samuel Mimram
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: Effects of Topology Knowledge and Relay Depth on Asynchronous Consensus
Consider an asynchronous incomplete directed network. We study the feasibility and efficiency of approximate crash-tolerant consensus under different restrictions on topology knowledge and relay depth, i.e., the maximum number of hops any message can be relayed.
Asynchrony
crash fault
consensus
topology knowledge
relay
Computer systems organization~Fault-tolerant network topologies
51:1-51:4
Brief Announcement
https://arxiv.org/abs/1803.04513
Dimitris
Sakavalas
Dimitris Sakavalas
Boston College, USA
Lewis
Tseng
Lewis Tseng
Boston College, USA
Nitin H.
Vaidya
Nitin H. Vaidya
Georgetown University, USA
This research is supported in part by National Science Foundation awards 1421918. Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the funding agencies or the U.S. government.
10.4230/LIPIcs.DISC.2018.51
Eduardo A. P. Alchieri, Alysson Neves Bessani, Joni da Silva Fraga, and Fabíola Greve. Byzantine consensus with unknown participants. In OPODIS 2008, volume 5401 of LNCS, pages 22-40. Springer, 2008. URL: http://dx.doi.org/10.1007/978-3-540-92221-6_4.
http://dx.doi.org/10.1007/978-3-540-92221-6_4
Danny Dolev. The Byzantine generals strike again. Journal of Algorithms, 3(1), 1982.
Danny Dolev, Nancy A. Lynch, Shlomit S. Pinter, Eugene W. Stark, and William E. Weihl. Reaching approximate agreement in the presence of faults. J. ACM, 33(3):499-516, 1986. URL: http://dx.doi.org/10.1145/5925.5931.
http://dx.doi.org/10.1145/5925.5931
M. Pease, R. Shostak, and L. Lamport. Reaching agreement in the presence of faults. J. ACM, 27(2):228-234, 1980. URL: http://dx.doi.org/10.1145/322186.322188.
http://dx.doi.org/10.1145/322186.322188
Dimitris Sakavalas, Lewis Tseng, and Nitin H. Vaidya. Effects of topology knowledge and relay depth on asynchronous consensus. CoRR, abs/1803.04513, 2018. URL: http://arxiv.org/abs/1803.04513.
http://arxiv.org/abs/1803.04513
Lili Su and Nitin Vaidya. Reaching approximate Byzantine consensus with multi-hop communication. In SSS 2015, volume 9212 of LNCS, pages 21-35. Springer, 2015. URL: http://dx.doi.org/10.1007/978-3-319-21741-3_2.
http://dx.doi.org/10.1007/978-3-319-21741-3_2
Lewis Tseng and Nitin H. Vaidya. Fault-tolerant consensus in directed graphs. In PODC '15, pages 451-460. ACM, 2015. URL: http://dx.doi.org/10.1145/2767386.2767399.
http://dx.doi.org/10.1145/2767386.2767399
Dimitris Sakavalas, Lewis Tseng, and Nitin H. Vaidya
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Brief Announcement: Loosely-stabilizing Leader Election with Polylogarithmic Convergence Time
We present a fast loosely-stabilizing leader election protocol in the population protocol model. It elects a unique leader in a poly-logarithmic time and holds the leader for a polynomial time with arbitrarily large degree in terms of parallel time, i.e, the number of steps per the population size.
Self-stabilization
Loose-stabilization
Population protocols
Theory of computation~Self-organization
52:1-52:3
Brief Announcement
Yuichi
Sudo
Yuichi Sudo
Graduate School of Information Science and Technology, Osaka University, Japan
Fukuhito
Ooshita
Fukuhito Ooshita
Graduate School of Science and Technology, Nara Institute of Science and Technology, Japan
Hirotsugu
Kakugawa
Hirotsugu Kakugawa
Graduate School of Information Science and Technology, Osaka University, Japan
Toshimitsu
Masuzawa
Toshimitsu Masuzawa
Graduate School of Information Science and Technology, Osaka University, Japan
10.4230/LIPIcs.DISC.2018.52
D. Angluin, J Aspnes, Z. Diamadi, M.J. Fischer, and R. Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Computing, 18(4):235-253, 2006.
T. Izumi. On space and time complexity of loosely-stabilizing leader election. In SIROCCO, pages 299-312, 2015.
Y. Sudo, J. Nakamura, Y. Yamauchi, F. Ooshita, et al. Loosely-stabilizing leader election in a population protocol model. Theoretical Computer Science, 444:100-112, 2012.
Y. Sudo, F. Ooshita, H. Kakugawa, and T. Masuzawa. Loosely-stabilizing leader election on arbitrary graphs in population protocols. In OPODIS, pages 339-354, 2014.
Yuichi Sudo, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode