Fast Convergence of Quantized Consensus Using Metropolis Chains Over Static and Dynamic Networks

We consider the quantized consensus problem on undirected connected graphs with n nodes, and devise a protocol with fast convergence time to the set of consensus points. Specifically, we show that when the edges of a static network are activated based on Poisson processes with Metropolis rates, the expected convergence time to the set of consensus points is at most O(n^2 log n). We further show an upper bound of O(n^2 log^2 n) for the expected convergence time of the same protocol over connected time-varying networks. These bounds are better than all previous convergence times for randomized quantized consensus.