The problem addressed in this paper is the analysis of a distributed
consensus algorithm for arbitrary networks, proposed by B\'en\'ezit et al.. In
the initial setting, each node in the network has one of two possible states
("yes" or "no"). Nodes can update their states by communicating with their
neighbors via a 2-bit message in an asynchronous clock setting. Eventually, all
nodes reach consensus on the majority states. We use the theory of electric
networks, random walks, and couplings of Markov chains to derive an O(N4 logN)
upper bound for the expected convergence time on an arbitrary graph of size N.Comment: 15th International Conference on Information Fusion, July 2012, 7
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