Lower Bounds for Randomized Consensus under a Weak Adversary

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 1 ck , for some constant c. 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. [22], for message-passing systems, and of Aumann et al. [6,7], for shared-memory systems. Categories and Subject Descriptors

• Type: Journal
• Year: 2010
• Where: SIAMCOMP
• Authors: Hagit Attiya, Keren Censor-Hillel
• Keywords: Algorithms, Consensus Algorithm, Et Al, SIAMCOMP 2010