Fast Consensus Protocols in the Asynchronous Poisson Clock Model with Edge Latencies
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We study the problem of distributed plurality consensus among n nodes, each of which initially holds one of k opinions. The goal is to eventually agree on the initially dominant opinion. We first describe our algorithm for the synchronous case and then extend it to the following asynchronous model. Every node is equipped with a random Poisson clock that ticks at constant rate. Upon a tick, the node may open constantly many communication channels to other nodes. The time for establishing a channel is exponentially distributed with constant mean. Once the channel is established, nodes may exchange messages and update their opinions. A simple clustering algorithm is used and each cluster contains a designated leader. These cluster leaders coordinate the progress of the distributed computation. We show that for k < n^1/2-ε, ε constant, and initial multiplicative bias α≥ 1 + kn/√(n)·k all but an 1/^O(1)n fraction of nodes converge towards the initial plurality opinion in O(_αk ·k + n) time whp., and all nodes have the initial plurality opinion after additional O(n) time whp. To achieve this result, we first derive an algorithm for a system with a designated leader, and then extend our approach to a distributed system without a leader.
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