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Brief Announcement: The Space Complexity of Set Agreement Using Swap

Author Sean Ovens



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Sean Ovens
  • University of Toronto, Canada

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Sean Ovens. Brief Announcement: The Space Complexity of Set Agreement Using Swap. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 46:1-46:6, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.DISC.2023.46

Abstract

We prove that any randomized wait-free n-process k-set agreement algorithm using only swap objects requires at least ⌈n/k⌉-1 objects. We also sketch a proof that any randomized wait-free consensus algorithm using only readable swap objects with domain size b requires at least (n-2)/(3b+1) objects.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • space complexity
  • consensus
  • set agreement
  • lower bound
  • shared memory

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References

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  2. Zohir Bouzid, Michel Raynal, and Pierre Sutra. Anonymous obstruction-free (n, k)-set agreement with n-k+1 atomic read/write registers. Distributed Comput., 31(2):99-117, 2018. URL: https://doi.org/10.1007/s00446-017-0301-7.
  3. Jack R. Bowman. Obstruction-free snapshot, obstruction-free consensus, and fetch-and-add modulo k. Master’s thesis, Dartmouth College, Computer Science, 2011. URL: https://digitalcommons.dartmouth.edu/senior_theses/67.
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  5. B. Chor, A. Israeli, and M. Li. Wait-free consensus using asynchronous hardware. SIAM J. Comput., 23:701-712, 1994. Google Scholar
  6. Faith Ellen, Rati Gelashvili, and Leqi Zhu. Revisionist simulations: A new approach to proving space lower bounds. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC '18, pages 61-70, New York, NY, USA, 2018. Association for Computing Machinery. URL: https://doi.org/10.1145/3212734.3212749.
  7. Faith Fich, Maurice Herlihy, and Nir Shavit. On the space complexity of randomized synchronization. J. ACM, 45(5):843-862, September 1998. A preliminary version appeared in PODC '93. URL: https://doi.org/10.1145/290179.290183.
  8. Sean Ovens. The space complexity of consensus from swap. In Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing, PODC'22, pages 176-186, New York, NY, USA, 2022. Association for Computing Machinery. URL: https://doi.org/10.1145/3519270.3538420.
  9. Sean Ovens. The space complexity of consensus from swap. CoRR, abs/2305.06507, 2023. URL: https://arxiv.org/abs/2305.06507.
  10. Leqi Zhu. A tight space bound for consensus. SIAM J. Comput., 50(3), 2019. A preliminary version appeared in STOC '16. URL: https://doi.org/10.1137/16M1096785.
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