Divide and Concur: Employing Chandra and Toueg’s Consensus Algorithm in a Multi-level Setting

Abstract

We revisit the work of Chandra and Toueg on achieving consensus using unreliable failure detectors in an asynchronous system with crash stop failures. Following a brief review of their approach, we provide a probabilistic analysis of their consensus algorithm, which shows that the number of messages is exponentially proportional to the number of participating processes n. Based on our analysis, we study how their solution may be improved when we have a priori knowledge of the maximum number of process failures that may occur. Accordingly, we propose multi-level consensus as a generalization of the Chandra-Toueg algorithm, and give a probabilistic analysis of our algorithm. For n large relative to the bound on the number of failures k, this approach yields an improvement (in the expected case) in the message complexity.