skip to main content
10.1145/3491003.3491005acmotherconferencesArticle/Chapter ViewAbstractPublication PagesicdcnConference Proceedingsconference-collections
research-article

Message Complexity of Multi-Valued Implicit Agreement with Shared Random Bits

Authors Info & Claims
Published:24 January 2022Publication History

ABSTRACT

An agreement protocol enables a system of n nodes in a distributed network to agree on a common input value. In the implicit version of the problem, only a subset of the nodes are required to decide the common value. This paper focuses on the message complexity of randomized implicit agreement in synchronous distributed networks. It has been shown by Augustine et al. [PODC 2018] that if the nodes have access to a shared coin, then implicit agreement can be solved with high probability1 using messages2 in expectation. However, their algorithm works only for binary input values, i.e, the input values given to the nodes are from the set {0, 1}. In this paper, we extended the result to the multi-valued setting where the input values may come from a larger but constant sized domain. We present an algorithm that solves the multi-valued implicit agreement problem with matching performance guarantees as in binary agreement.

References

  1. Ittai Abraham, Danny Dolev, and Joseph Y. Halpern. 2008. An almost-surely terminating polynomial protocol forasynchronous byzantine agreement with optimal resilience. In Proceedings of the Twenty-Seventh Annual ACM Symposium on Principles of Distributed Computing, PODC 2008, Toronto, Canada, August 18-21, 2008, Rida A. Bazzi and Boaz Patt-Shamir (Eds.). ACM, 405–414. https://doi.org/10.1145/1400751.1400804Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Yair Amir, Claudiu Danilov, Jonathan Kirsch, John Lane, Danny Dolev, Cristina Nita-Rotaru, Josh Olsen, and David John Zage. 2006. Scaling Byzantine Fault-Tolerant Replication toWide Area Networks. In 2006 International Conference on Dependable Systems and Networks (DSN 2006), 25-28 June 2006, Philadelphia, Pennsylvania, USA, Proceedings. IEEE Computer Society, 105–114. https://doi.org/10.1109/DSN.2006.63Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. John Augustine, Anisur Rahaman Molla, and Gopal Pandurangan. 2018. Sublinear Message Bounds for Randomized Agreement. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC 2018, Egham, United Kingdom, July 23-27, 2018, Calvin Newport and Idit Keidar (Eds.). ACM, 315–324. https://dl.acm.org/citation.cfm?id=3212751Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Michael Ben-Or and Avinatan Hassidim. 2005. Fast quantum byzantine agreement. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, May 22-24, 2005, Harold N. Gabow and Ronald Fagin (Eds.). ACM, 481–485. https://doi.org/10.1145/1060590.1060662Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Michael Ben-Or, Elan Pavlov, and Vinod Vaikuntanathan. 2006. Byzantine agreement in the full-information model in O(log n) rounds. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, USA, May 21-23, 2006, Jon M. Kleinberg (Ed.). ACM, 179–186. https://doi.org/10.1145/1132516.1132543Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Gabriel Bracha. 1984. An Asynchronou [(n-1)/3]-Resilient Consensus Protocol. In Proceedings of the Third Annual ACM Symposium on Principles of Distributed Computing, Vancouver, B. C., Canada, August 27-29, 1984, Tiko Kameda, Jayadev Misra, Joseph G. Peters, and Nicola Santoro (Eds.). ACM, 154–162. https://doi.org/10.1145/800222.806743Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Gabriel Bracha. 1987. Asynchronous Byzantine Agreement Protocols. Inf. Comput. 75, 2 (1987), 130–143. https://doi.org/10.1016/0890-5401(87)90054-XGoogle ScholarGoogle ScholarDigital LibraryDigital Library
  8. Gabriel Bracha. 1987. An O(log n) expected rounds randomized byzantine generals protocol. J. ACM 34, 4 (1987), 910–920. https://doi.org/10.1145/31846.42229Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Nicolas Braud-Santoni, Rachid Guerraoui, and Florian Huc. 2013. Fast byzantine agreement. In ACM Symposium on Principles of Distributed Computing, PODC ’13, Montreal, QC, Canada, July 22-24, 2013, Panagiota Fatourou and Gadi Taubenfeld (Eds.). ACM, 57–64.Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Miguel Castro and Barbara Liskov. 2002. Practical byzantine fault tolerance and proactive recovery. ACM Trans. Comput. Syst. 20, 4 (2002), 398–461. https://doi.org/10.1145/571637.571640Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Luc Devroye. 2006. Nonuniform random variate generation. Handbooks in operations research and management science 13 (2006), 83–121.Google ScholarGoogle Scholar
  12. Danny Dolev and H. Raymond Strong. 1983. Authenticated Algorithms for Byzantine Agreement. SIAM J. Comput. 12, 4 (1983), 656–666. https://doi.org/10.1137/0212045Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Paul Feldman and Silvio Micali. 1988. Optimal Algorithms for Byzantine Agreement. In Proceedings of the 20th Annual ACM Symposium on Theory of Computing, May 2-4, 1988, Chicago, Illinois, USA, Janos Simon (Ed.). ACM, 148–161. https://doi.org/10.1145/62212.62225Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Valerie King and Jared Saia. 2011. Breaking the O(n2) bit barrier: Scalable byzantine agreement with an adaptive adversary. J. ACM 58, 4 (2011), 18:1–18:24. https://doi.org/10.1145/1989727.1989732Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Valerie King and Jared Saia. 2016. Byzantine Agreement in Expected Polynomial Time. J. ACM 63, 2 (2016), 13:1–13:21. https://doi.org/10.1145/2837019Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. 2015. On the Complexity of Universal Leader Election. J. ACM 62, 1 (2015), 7:1–7:27. https://doi.org/10.1145/2699440Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. 2015. Sublinear bounds for randomized leader election. Theor. Comput. Sci. 561(2015), 134–143. https://doi.org/10.1016/j.tcs.2014.02.009Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Leslie Lamport, Robert E. Shostak, and Marshall C. Pease. 1982. The Byzantine Generals Problem. ACM Trans. Program. Lang. Syst. 4, 3 (1982), 382–401. https://doi.org/10.1145/357172.357176Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Dahlia Malkhi and Michael K. Reiter. 1997. Unreliable Intrusion Detection in Distributed Computations. In 10th Computer Security Foundations Workshop (CSFW ’97), June 10-12, 1997, Rockport, Massachusetts, USA. IEEE Computer Society, 116–125. https://doi.org/10.1109/CSFW.1997.596799Google ScholarGoogle Scholar
  20. Michael Mitzenmacher and Eli Upfal. 2017. Probability and computing: Randomization and probabilistic techniques in algorithms and data analysis. Cambridge university press.Google ScholarGoogle Scholar
  21. Marshall C. Pease, Robert E. Shostak, and Leslie Lamport. 1980. Reaching Agreement in the Presence of Faults. J. ACM 27, 2 (1980), 228–234.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. David Peleg. 2000. Distributed Computing: A Locality-Sensitive Approach. SIAM, Philadelphia.Google ScholarGoogle ScholarCross RefCross Ref
  23. Michael O. Rabin. 1983. Randomized Byzantine Generals. In 24th Annual Symposium on Foundations of Computer Science, Tucson, Arizona, USA, 7-9 November 1983. IEEE Computer Society, 403–409. https://doi.org/10.1109/SFCS.1983.48Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Duncan M’Laren Young Sommerville. 2020. Introduction to the Geometry of N Dimensions. Courier Dover Publications.Google ScholarGoogle Scholar
  25. Hiroyuki Yoshino, Naohiro Hayashibara, Tomoya Enokido, and Makoto Takizawa. 2005. Byzantine Agreement Protocol using Hierarchical Groups. In 11th International Conference on Parallel and Distributed Systems, ICPADS 2005, Fuduoka, Japan, July 20-22, 2005. IEEE Computer Society, 64–70. https://doi.org/10.1109/ICPADS.2005.104Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Message Complexity of Multi-Valued Implicit Agreement with Shared Random Bits
        Index terms have been assigned to the content through auto-classification.

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in
        • Published in

          cover image ACM Other conferences
          ICDCN '22: Proceedings of the 23rd International Conference on Distributed Computing and Networking
          January 2022
          298 pages
          ISBN:9781450395601
          DOI:10.1145/3491003

          Copyright © 2022 ACM

          Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 24 January 2022

          Permissions

          Request permissions about this article.

          Request Permissions

          Check for updates

          Qualifiers

          • research-article
          • Research
          • Refereed limited
        • Article Metrics

          • Downloads (Last 12 months)8
          • Downloads (Last 6 weeks)1

          Other Metrics

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader

        HTML Format

        View this article in HTML Format .

        View HTML Format