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The Time Complexity of Consensus Under Oblivious Message Adversaries

Authors Kyrill Winkler , Ami Paz , Hugo Rincon Galeana , Stefan Schmid , Ulrich Schmid

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Author Details

Kyrill Winkler
  • ITK Engineering, Wien, Austria
Ami Paz
  • LISN - CNRS & Paris-Saclay University, France
Hugo Rincon Galeana
  • TU Wien, Austria
Stefan Schmid
  • TU Berlin, Germany
  • Fraunhofer SIT, Darmstadt, Germany
Ulrich Schmid
  • TU Wien, Austria

Funding

This research has received funding from the German Federal Ministry of Education and Research (BMBF), 6G-RIC, grant 16KISK020K; Vienna Science and Technology Fund (WWTF) project ICT19-045; Austrian Science Fund (FWF) projects ADynNet P28182, ByzDEL P33600, and netIDEE SCIENCE P33775-N.
  • Winkler, Kyrill: Vienna Science and Technology Fund (WWTF) project ICT19-045, 2020-2024.
  • Rincon Galeana, Hugo: Supported by the Doctoral College on Resilient Embedded Systems at TU Wien.

Cite As Get BibTex

Kyrill Winkler, Ami Paz, Hugo Rincon Galeana, Stefan Schmid, and Ulrich Schmid. The Time Complexity of Consensus Under Oblivious Message Adversaries. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 100:1-100:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ITCS.2023.100

Abstract

We study the problem of solving consensus in synchronous directed dynamic networks, in which communication is controlled by an oblivious message adversary that picks the communication graph to be used in a round from a fixed set of graphs 𝐃 arbitrarily. In this fundamental model, determining consensus solvability and designing efficient consensus algorithms is surprisingly difficult. Enabled by a decision procedure that is derived from a well-established previous consensus solvability characterization for a given set 𝐃, we study, for the first time, the time complexity of solving consensus in this model: We provide both upper and lower bounds for this time complexity, and also relate it to the number of iterations required by the decision procedure. Among other results, we find that reaching consensus under an oblivious message adversary can take exponentially longer than both deciding consensus solvability and broadcasting the input value of some unknown process to all other processes.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Networks
Keywords
  • dynamic networks
  • oblivious message adversaries
  • consensus
  • time complexity

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References

  1. Ittai Abraham, Dahlia Malkhi, et al. The blockchain consensus layer and BFT. Bulletin of EATCS, 3(123), 2017. Google Scholar
  2. Yehuda Afek and Eli Gafni. Asynchrony from synchrony. In Distributed Computing and Networking, volume 7730 of Lecture Notes in Computer Science, pages 225-239. Springer Berlin Heidelberg, 2013. URL: https://doi.org/10.1007/978-3-642-35668-1_16.
  3. Hagit Attiya and Armando Castañeda. A non-topological proof for the impossibility of k-set agreement. Theor. Comput. Sci., 512:41-48, 2013. Google Scholar
  4. Hagit Attiya, Armando Castañeda, Maurice Herlihy, and Ami Paz. Bounds on the step and namespace complexity of renaming. SIAM J. Comput., 48(1):1-32, 2019. URL: https://doi.org/10.1137/16M1081439.
  5. Martin Biely, Peter Robinson, and Ulrich Schmid. Agreement in directed dynamic networks. In Proceedings 19th International Colloquium on Structural Information and Communication Complexity (SIROCCO'12), LNCS 7355, pages 73-84. Springer-Verlag, 2012. URL: https://doi.org/10.1007/978-3-642-31104-8_7.
  6. 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. URL: https://doi.org/10.1016/j.tcs.2018.02.019.
  7. Martin Biely, Ulrich Schmid, and Bettina Weiss. Synchronous consensus under hybrid process and link failures. Theoretical Computer Science, 412(40):5602-5630, 2011. http://dx.doi.org/10.1016/j.tcs.2010.09.032. URL: http://www.sciencedirect.com/science/article/pii/S0304397510005359.
  8. Ofer Biran, Shlomo Moran, and Shmuel Zaks. A combinatorial characterization of the distributed 1-solvable tasks. Journal of algorithms, 11(3):420-440, 1990. Google Scholar
  9. Armando Castañeda, Pierre Fraigniaud, Ami Paz, Sergio Rajsbaum, Matthieu Roy, and Corentin Travers. A topological perspective on distributed network algorithms. In Structural Information and Communication Complexity - 26th International Colloquium, SIROCCO, pages 3-18, 2019. URL: https://doi.org/10.1007/978-3-030-24922-9_1.
  10. Bernadette Charron-Bost, Matthias Függer, and Thomas Nowak. Approximate consensus in highly dynamic networks: The role of averaging algorithms. In Automata, Languages, and Programming, volume 9135 of Lecture Notes in Computer Science, pages 528-539. Springer Berlin Heidelberg, 2015. URL: https://doi.org/10.1007/978-3-662-47666-6_42.
  11. Bernadette Charron-Bost and André Schiper. The Heard-Of model: computing in distributed systems with benign faults. Distributed Computing, 22(1):49-71, April 2009. URL: https://doi.org/10.1007/s00446-009-0084-6.
  12. Étienne Coulouma, Emmanuel Godard, and Joseph G. Peters. A characterization of oblivious message adversaries for which consensus is solvable. Theor. Comput. Sci., 584:80-90, 2015. URL: https://doi.org/10.1016/j.tcs.2015.01.024.
  13. Antoine El-Hayek, Monika Henzinger, and Stefan Schmid. Brief announcement: Broadcasting time in dynamic rooted trees is linear. In Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing, PODC, 2022. Google Scholar
  14. Antoine El-Hayek, Monika Henzinger, and Stefan Schmid. Asymptotically tight bounds on the time complexity of broadcast and its variants in dynamic networks. In 14th Innovations in Theoretical Computer Science (ITCS), 2023. Google Scholar
  15. Tristan Fevat and Emmanuel Godard. Minimal obstructions for the coordinated attack problem and beyond. In 25th IEEE International Symposium on Parallel and Distributed Processing, IPDPS 2011, Anchorage, Alaska, USA, 16-20 May, 2011 - Conference Proceedings, pages 1001-1011, 2011. URL: https://doi.org/10.1109/IPDPS.2011.96.
  16. Michael J. Fischer, Nancy A. Lynch, and M. S. Paterson. Impossibility of distributed consensus with one faulty process. Journal of the ACM, 32(2):374-382, April 1985. Google Scholar
  17. 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, New York, NY, USA, 2018. ACM. URL: https://doi.org/10.1145/3212734.3212762.
  18. Matthias Függer, Thomas Nowak, and Kyrill Winkler. On the radius of nonsplit graphs and information dissemination in dynamic networks. Discrete Applied Mathematics, 282:257-264, 2020. URL: https://doi.org/10.1016/j.dam.2020.02.013.
  19. Eli Gafni. Round-by-round fault detectors (extended abstract): unifying synchrony and asynchrony. In Proceedings of the Seventeenth Annual ACM Symposium on Principles of Distributed Computing, pages 143-152, Puerto Vallarta, Mexico, 1998. ACM Press. URL: https://doi.org/10.1145/277697.277724.
  20. Maurice Herlihy, Dmitry N. Kozlov, and Sergio Rajsbaum. Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, 2013. URL: https://store.elsevier.com/product.jsp?isbn=9780124045781.
  21. Idit Keidar and Alex Shraer. Timeliness, failure detectors, and consensus performance. In Proceedings of the twenty-fifth annual ACM SIGACT-SIGOPS symposium on Principles of Distributed Computing (PODC'06), pages 169-178, New York, NY, USA, 2006. ACM Press. Google Scholar
  22. Dmitry N. Kozlov. Structure theory of flip graphs with applications to weak symmetry breaking. CoRR, abs/1511.00457, 2015. URL: http://arxiv.org/abs/1511.00457.
  23. Dmitry N. Kozlov. Combinatorial Topology of the Standard Chromatic Subdivision and Weak Symmetry Breaking for Six Processes, pages 155-194. Springer International Publishing, Cham, 2016. URL: https://doi.org/10.1007/978-3-319-31580-5_7.
  24. F. Kuhn and R. Oshman. Dynamic networks: Models and algorithms. SIGACT News, 42(1):82-96, 2011. Google Scholar
  25. Fabian Kuhn, Nancy A. Lynch, and Rotem Oshman. Distributed computation in dynamic networks. In STOC, pages 513-522, 2010. URL: https://doi.org/10.1145/1806689.1806760.
  26. Fabian Kuhn, Rotem Oshman, and Yoram Moses. Coordinated consensus in dynamic networks. In Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing, PODC '11. ACM, 2011. Google Scholar
  27. Calvin Newport, David Kotz, Yougu Yuan, Robert S. Gray, Jason Liu, and Chip Elliott. Experimental Evaluation of Wireless Simulation Assumptions. SIMULATION: Transactions of The Society for Modeling and Simulation International, 83(9):643-661, September 2007. URL: https://doi.org/10.1177/0037549707085632.
  28. Thomas Nowak, Ulrich Schmid, and Kyrill Winkler. Topological characterization of consensus under general message adversaries. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, PODC 2019, Toronto, ON, Canada, July 29 - August 2, 2019., pages 218-227, 2019. (full version: http://arxiv.org/abs/1905.09590). URL: https://doi.org/10.1145/3293611.3331624.
  29. Diego Ongaro and John Ousterhout. In search of an understandable consensus algorithm. In Proc. USENIX Annual Technical Conference (ATC), pages 305-319, 2014. Google Scholar
  30. Nicola Santoro and Peter Widmayer. Time is not a healer. In Proc. 6th Annual Symposium on Theor. Aspects of Computer Science (STACS'89), LNCS 349, pages 304-313, Paderborn, Germany, February 1989. Springer-Verlag. Google Scholar
  31. Nicola Santoro and Peter Widmayer. Agreement in synchronous networks with ubiquitous faults. Theoretical Computer Science, 384(2-3):232-249, October 2007. Google Scholar
  32. 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. URL: https://doi.org/10.1137/S009753970443999X.
  33. Manfred Schwarz, Kyrill Winkler, and Ulrich Schmid. Fast consensus under eventually stabilizing message adversaries. In Proceedings of the 17th International Conference on Distributed Computing and Networking, ICDCN '16, pages 7:1-7:10, New York, NY, USA, 2016. ACM. URL: https://doi.org/10.1145/2833312.2833323.
  34. Kyrill Winkler and Ulrich Schmid. An overview of recent results for consensus in directed dynamic networks. Bulletin of the EATCS, 128, 2019. URL: http://bulletin.eatcs.org/index.php/beatcs/article/view/581.
  35. Kyrill Winkler, Ulrich Schmid, and Yoram Moses. A characterization of consensus solvability for closed message adversaries. In 23rd International Conference on Principles of Distributed Systems, OPODIS, volume 153 of LIPIcs, pages 17:1-17:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2019.17.
  36. Kyrill Winkler, Manfred Schwarz, and Ulrich Schmid. Consensus in directed dynamic networks with short-lived stability. Distributed Computing, 32(5):443-458, 2019. URL: https://doi.org/10.1007/s00446-019-00348-0.
  37. Martin Zeiner, Manfred Schwarz, and Ulrich Schmid. On linear-time data dissemination in dynamic rooted trees. Discrete Applied Mathematics, 255:307-319, 2019. URL: https://doi.org/10.1016/j.dam.2018.08.015.
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