Document Open Access Logo

Message Reduction in the LOCAL Model Is a Free Lunch

Authors Shimon Bitton, Yuval Emek, Taisuke Izumi, Shay Kutten

PDF
Thumbnail PDF

File

LIPIcs.DISC.2019.7.pdf
  • Filesize: 0.55 MB
  • 15 pages

Document Identifiers

Author Details

Shimon Bitton
  • Technion - Israel Institute of Technology, Haifa, Israel
Yuval Emek
  • Technion - Israel Institute of Technology, Haifa, Israel
Taisuke Izumi
  • Nagoya Institute of Technology, Japan
Shay Kutten
  • Technion - Israel Institute of Technology, Haifa, Israel

Funding

  • Emek, Yuval: This work has been funded in part by an Israeli Ministry of Science and Technology grant number 3-13565.
  • Izumi, Taisuke: This work was supported by JST SICORP Grant Number JPMJSC1606 and JSPS KAKENHI Grant Number JP19K11824, Japan.
  • Kutten, Shay: This work has been funded in part by an Israeli Ministry of Science and Technology grant number 3-13565.

Cite As Get BibTex

Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Message Reduction in the LOCAL Model Is a Free Lunch. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.DISC.2019.7

Abstract

A new spanner construction algorithm is presented, working under the LOCAL model with unique edge IDs. Given an n-node communication graph, a spanner with a constant stretch and O(n^{1 + epsilon}) edges (for an arbitrarily small constant epsilon > 0) is constructed in a constant number of rounds sending O(n^{1 + epsilon}) messages whp. Consequently, we conclude that every t-round LOCAL algorithm can be transformed into an O(t)-round LOCAL algorithm that sends O(t * n^{1 + epsilon}) messages whp. This improves upon all previous message-reduction schemes for LOCAL algorithms that incur a log^{Omega (1)} n blow-up of the round complexity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Sparsification and spanners
  • Theory of computation → Distributed algorithms
Keywords
  • distributed graph algorithms
  • spanner
  • LOCAL model
  • message complexity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Baruch Awerbuch. Complexity of network synchronization. Journal of the ACM (JACM), 32(4):804-823, 1985. URL: https://doi.org/10.1145/4221.4227.
  2. Baruch Awerbuch, Bonnie Berger, Lenore Cowen, and David Peleg. Near-linear time construction of sparse neighborhood covers. SIAM Journal on Computing (SICOMP), 28(1):263-277, 1998. URL: https://doi.org/10.1137/S0097539794271898.
  3. 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. URL: https://doi.org/10.1145/77600.77618.
  4. Leonid Barenboim, Michael Elkin, and Cyril Gavoille. A fast network-decomposition algorithm and its applications to constant-time distributed computation. Theoretical Computer Science, 751:2-23, 2018. URL: https://doi.org/10.1016/j.tcs.2016.07.005.
  5. 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. URL: https://doi.org/10.1002/rsa.v30:4.
  6. 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. URL: https://doi.org/10.1007/s00224-013-9444-5.
  7. Keren Censor-Hillel and Michal Dory. Distributed Spanner Approximation. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing (PODC), pages 139-148, 2018. URL: https://doi.org/10.1145/3212734.3212758.
  8. 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 (STOC), pages 961-970, 2012. URL: https://doi.org/10.1145/2213977.2214064.
  9. Bilel Derbel and Cyril Gavoille. Fast Deterministic Distributed Algorithms for Sparse Spanners. Theoretical Computer Science, 399(1):83-100, 2008. URL: https://doi.org/10.1016/j.tcs.2008.02.019.
  10. 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 (PODC), pages 273-282, 2008. URL: https://doi.org/10.1145/1400751.1400788.
  11. Bilel Derbel, Cyril Gavoille, David Peleg, and Laurent Viennot. Local Computation of Nearly Additive Spanners. In Proceedings of 23rd International Symposium on Distributed Computing (DISC), pages 176-190, 2009. URL: https://doi.org/10.1007/978-3-642-04355-0_20.
  12. Devdatt Dubhashi, Alessandro Mei, Alessandro Panconesi, Jaikumar Radhakrishnan, and Aravind Srinivasan. Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons. Journal of Computer and System Sciences, 71(4):467-479, 2005. URL: https://doi.org/10.1016/j.jcss.2005.04.002.
  13. Michael Elkin. Computing Almost Shortest Paths. ACM Transactions on Algorithms (TALG), 1(2):283-323, 2005. URL: https://doi.org/10.1145/1103963.1103968.
  14. Michael Elkin. A near-optimal distributed fully dynamic algorithm for maintaining sparse spanners. In Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing (PODC), pages 185-194, 2007. URL: https://doi.org/10.1145/1281100.1281128.
  15. Michael Elkin and Ofer Neiman. Distributed Strong Diameter Network Decomposition: Extended Abstract. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing (PODC), pages 211-216, 2016. URL: https://doi.org/10.1145/2933057.2933094.
  16. Michael Elkin and Ofer Neiman. Efficient Algorithms for Constructing Very Sparse Spanners and Emulators. ACM Transactions on Algorithms (TALG), 15(1):4:1-4:29, 2018. URL: https://doi.org/10.1145/3274651.
  17. Michael Elkin and David Peleg. (1+ε, β)-Spanner Constructions for General Graphs. SIAM Journal on Computing, 33(3):608-631, 2004. URL: https://doi.org/10.1137/S0097539701393384.
  18. Michael Elkin and Jian Zhang. Efficient algorithms for constructing (1+ε, β)-spanners in the distributed and streaming models. Distributed Computing, 18(5):375-385, 2006. URL: https://doi.org/10.1007/s00446-005-0147-2.
  19. Mohsen Ghaffari and Fabian Kuhn. Distributed MST and Broadcast with Fewer Messages, and Faster Gossiping. In Proceedings of 32nd International Symposium on Distributed Computing (DISC), volume 121, pages 30:1-30:12, 2018. URL: https://doi.org/10.4230/LIPIcs.DISC.2018.30.
  20. Mohsen Ghaffari, Fabian Kuhn, and Yannic Maus. On the complexity of local distributed graph problems. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (STOC), pages 784-797, 2017. URL: https://doi.org/10.1145/3055399.3055471.
  21. Robert Gmyr and Gopal Pandurangan. Time-Message Trade-Offs in Distributed Algorithms. In Proceedings of 32nd International Symposium on Distributed Computing, (DISC), volume 121, pages 32:1-32:18, 2018. URL: https://doi.org/10.4230/LIPIcs.DISC.2018.32.
  22. Bernhard Haeupler. Simple, Fast and Deterministic Gossip and Rumor Spreading. Journal of the ACM (JACM), 62(6):47:1-47:18, December 2015. URL: https://doi.org/10.1145/2767126.
  23. 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), pages 71-80, 2015. URL: https://doi.org/10.1145/2767386.2767405.
  24. Ephraim Korach, Shay Kutten, and Shlomo Moran. A modular technique for the design of efficient distributed leader finding algorithms. ACM Transactions on Programming Languages and Systems (TOPLAS), 12(1):84-101, 1990. URL: https://doi.org/10.1145/323596.323611.
  25. 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):7:1-7:27, 2015. URL: https://doi.org/10.1145/2699440.
  26. Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. Sublinear bounds for randomized leader election. Theoretical Computer Science, 561:134-143, 2015. URL: https://doi.org/10.1016/j.tcs.2014.02.009.
  27. Nathan Linial. Locality in Distributed Graph Algorithms. SIAM Journal on Computing (SICOMP), 21(1):193-201, 1992. URL: https://doi.org/10.1137/0221015.
  28. Nathan Linial and Michael Saks. Low diameter graph decompositions. Combinatorica, 13(4):441-454, 1993. URL: https://doi.org/10.1007/BF01303516.
  29. Ali Mashreghi and Valerie King. Broadcast and minimum spanning tree with o(m) messages in the asynchronous CONGEST model. In Proceedings of 32nd International Symposium on Distributed Computing (DISC), pages 37:1-37:17, 2018. URL: https://doi.org/10.4230/LIPIcs.DISC.2018.37.
  30. Gary L. Miller, Richard Peng, Adrian Vladu, and Shen Chen Xu. Improved Parallel Algorithms for Spanners and Hopsets. In Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 192-201, 2015. URL: https://doi.org/10.1145/2755573.2755574.
  31. David Peleg. Distributed Computing: A Locality-sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2000. URL: https://doi.org/10.1137/1.9780898719772.
  32. David Peleg and Alejandro A Schäffer. Graph spanners. Journal of Graph Theory, 13(1):99-116, 1989. URL: https://doi.org/10.1002/jgt.3190130114.
  33. David Peleg and Jeffrey D. Ullman. An Optimal Synchronizer for the Hypercube. SIAM Journal on Computing (SICOMP), 18(4):740-747, 1989. URL: https://doi.org/10.1137/0218050.
  34. David Peleg and Eli Upfal. A trade-off between space and efficiency for routing tables. Journal of the ACM (JACM), 36(3):510-530, 1989. URL: https://doi.org/10.1145/62212.62217.
  35. Seth Pettie. Distributed algorithms for ultrasparse spanners and linear size skeletons. Distributed Computing, 22(3):147-166, 2010. URL: https://doi.org/10.1007/s00446-009-0091-7.
  36. Mikkel Thorup and Uri Zwick. Approximate distance oracles. Journal of the ACM (JACM), 52(1):1-24, 2005. URL: https://doi.org/10.1145/1044731.1044732.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact