NDLI: Lower Bounds for Randomized Consensus under a Weak Adversary

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Attiya, Hagit Censor-Hillel, Keren
Copyright Year	2010
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. 10381047] 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. 209218] and Aumann and Bender [Distrib. Comput., 17 (2005), pp. 191207] for shared-memory systems.
Starting Page	3885
Ending Page	3904
Page Count	20
File Format	PDF
ISSN	00975397
DOI	10.1137/090751906
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	8
Volume Number	39
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-12-22
Access Restriction	Subscribed
Subject Keyword	consensus message passing Probability in computer science randomized algorithms Randomized algorithms Models and methods for concurrent and distributed computing lower bound Distributed algorithms distributed computing shared memory
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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