Asymptotically optimal distributed consensus

Abstract

The Distributed Consensus problem requires correct processors to reach consensus in the presence of the arbitrary behavior of t faulty processors. In this paper we present a protocol that achieves consensus with n>4t total processors using 2t+2 rounds of communication and messages of size 1. This is the first protocol in which all three parameters are simultaneously within a constant factor from their optima. Subsequently, we modify it to obtain a family of equally resilient protocols which use t(1 + 1/d) rounds and O(2d) message size, improving on previous results. Finally, we show that the first protocol can be adapted very efficiently to run on bounded-degree networks, so that consensus can be reached in the presence of O(n/log n) faulty processors in time O(n). It improves on the previous result, which implied that consensus can be reached in this setting in time Θ(n 3).