Fast convergence of quantized consensus using Metropolis chains

We consider the quantized consensus problem on undirected connected graphs and study its expected convergence time to the set of consensus points. As compared with earlier results on the problem, we improve the convergence speed of the dynamics by a factor of n, where n is the number of agents involved in the dynamics. In particular, we show that when the edges of the network are activated based on a Poisson processes with Metropolis rates, the expected convergence time to the consensus set is at most O(n² log n). This upper bound is better than all available results for randomized quantized consensus.