Multi-sided shared coins and randomized set-agreement

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(n 2 /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(n 2 /k + nk) and an individual step complexity of O(n/k + k). Next, other set-agreement algorithms for agreeing on values out of k + 1, where is smaller than k, are presented. This includes the case of multi-valued consensus in which = 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 = k = 1. Finally, an application of asynchronous wait-free multi-valued consensus is presented, in implementing atmost-once semantics with optimal effectiveness.

A modular approach to shared-memory consensus, with applications to the probabilistic-write model

“…Note that this implementation only provides a 2-valued conciliator. How to extend a shared coin to more values is not obvious; for one choice, see [26]. Our new algorithm below avoids this restriction to a bounded set of values, at the cost of requiring a weaker adversary.…”