Lower bounds for randomized consensus under a weak adversary

  • Authors:
  • Hagit Attiya;Keren Censor

  • Affiliations:
  • Technion, Haifa, Israel;Technion, Haifa, Israel

  • Venue:
  • Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
  • Year:
  • 2008

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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 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. (SODA 2008), for message-passing systems, and of Aumann et al. (PODC 1997, Distributed Computing 2005), for shared-memory systems.