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 logn). We further show an upper bound of O(n log 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.