Consensus with quantized information updates

We study the distributed averaging problem on arbitrary connected graphs, with the additional constraint that the value at each node is an integer. This discretized distributed averaging problem models averaging in a network with finite capacity channels (and in this form has applications to. the computation of sufficient statistics in various sensing problems) and load balancing in a processor network. We describe simple randomized distributed algorithms which achieve consensus to the extent that the discrete nature of the problem permits. We obtain bounds on the convergence time of these algorithms for fully connected networks and linear networks.