Lower Bounds for Randomized Consensus under a Weak Adversary
Name
Attiya-2010-LOWER BOUNDS FOR RANDOMIZED CONSENSUS UNDER A WEAK ADVERSARY.pdf
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272.67 KB
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Author(s)
Attiya, Hagit
Censor-Hillel, Keren
Date Issued
December 2010
Journal
SIAM Journal on Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Attiya, Hagit, and Keren Censor-Hillel. “Lower Bounds for Randomized Consensus Under a Weak Adversary.” SIAM Journal on Computing 39.8 (2010) : 3885. © 2010 Society for Industrial and Applied Mathematics.
Version
Final published version
Abstract
This paper studies the inherent trade-off between termination probability and total step complexity of randomized consensus algorithms. It shows that for every integer $k$, the probability that an $f$-resilient randomized consensus algorithm of $n$ processes does not terminate with agreement within $k(n-f)$ steps is at least $\frac{1}{c^k}$, for some constant $c$. A corresponding result is proved for Monte-Carlo algorithms that may terminate in disagreement. The lower bound holds for asynchronous systems, where processes communicate either by message passing or through shared memory, under a very weak adversary that determines the schedule in advance, without observing the algorithm's actions. This complements algorithms of Kapron et al. [Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), ACM, New York, SIAM, Philadelphia, 2008, pp. 1038–1047] for message-passing systems, and of Aumann [Proceedings of the 16th Annual ACM Symposium on Principles of Distributed Computing (PODC), ACM, New York, 1997, pp. 209–218] and Aumann and Bender [Distrib. Comput., 17 (2005), pp. 191–207] for shared-memory systems.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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DOI of Published Version
https://doi.org/10.1137/090751906
