Stabilizing consensus with the power of two choices

  • Authors:

  • Benjamin Doerr;Leslie Ann Goldberg;Lorenz Minder;Thomas Sauerwald;Christian Scheideler

  • Affiliations:

  • Max Planck Institute for Informatics, Saarbrücken, Germany;University of Liverpool, Liverpool, United Kingdom;University of California, Berkeley, USA;Max Planck Institute for Informatics, Saarbrücken, Germany;University of Paderborn, Paderborn, Germany

  • Venue:
  • Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
  • Year:
  • 2011

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Abstract

In the standard consensus problem there are n processes with possibly different input values and the goal is to eventually reach a point at which all processes commit to exactly one of these values. We are studying a slight variant of the consensus problem called the stabilizing consensus problem [2]. In this problem, we do not require that each process commits to a final value at some point, but that eventually they arrive at a common, stable value without necessarily being aware of that. This should work irrespective of the states in which the processes are starting. Our main result is a simple randomized algorithm called median rule that, with high probability, just needs O(log m log log n + log n) time and work per process to arrive at an almost stable consensus for any set of m legal values as long as an adversary can corrupt the states of at most √n processes at any time. Without adversarial involvement, just O(log n) time and work is needed for a stable consensus, with high probability. As a by-product, we obtain a simple distributed algorithm for approximating the median of n numbers in time O(log m log log n + log n) under adversarial presence.