Multi-sided shared coins and randomized set-agreement

  • Authors:

  • Keren Censor Hillel

  • Affiliations:

  • Technion - Israel Institute of Technology, Haifa, Israel

  • Venue:
  • Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
  • Year:
  • 2010

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Abstract

This paper presents wait-free randomized algorithms for solving set-agreement in asynchronous shared-memory systems under a strong adversary. First, the definition of a shared-coin algorithm is generalized to a multi-sided shared-coin algorithm, and it is shown how to use any multi-sided shared coin in order to obtain a randomized set-agreement algorithm for agreeing on k values out of k+1. Then, an implementation is given for a (k+1)-sided shared coin for n processes with a constant agreement parameter, O(n2/k) total step complexity, and O(n/k) individual step complexity. This implementation yields a randomized set-agreement algorithm for agreeing on k values out of k+1 with a total step complexity of O(n2/k + nk) and an individual step complexity of O(n/k + k). Next, other set-agreement algorithms for agreeing on l values out of k+1, where l is smaller than k, are presented. This includes the case of multi-valued consensus in which l=1, k 1. To the best of our knowledge, these are the first wait-free algorithms for set-agreement in the asynchronous shared-memory model under a strong adversary that are not for the specific case of binary consensus, where l= k = 1. Finally, an application of asynchronous wait-free multi-valued consensus is presented, in implementing at-most-once semantics with optimal effectiveness.