Fast decentralized averaging via multi-scale gossip

Abstract

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(n1/3) hops, our algorithm is robust and has communication cost of O(n loglogn logε-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. © 2010 Springer-Verlag.