Fast Decentralized Averaging via Multi-scale Gossip

We are interested in the problem of computing the average consensus in a distributed fashion on random geometric graphs. We describe a new algorithm called Multi-scale Gossip which employs a hierarchical decomposition of the graph to partition the computation into tractable sub-problems. Using only pairwise messages of fixed size that travel at most O(n 1 3 ) hops, our algorithm is robust and has communication cost of O(n log logn log −1) transmissions, which is order-optimal up to the logarithmic factor in n. Simulated experiments verify the good expected performance on graphs of many thousands of nodes.