Fast decentralized averaging via multi-scale gossip

Authors:
Konstantinos I. Tsianos;Michael G. Rabbat
Affiliations:
Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada;Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada
Venue:
DCOSS'10 Proceedings of the 6th IEEE international conference on Distributed Computing in Sensor Systems
Year:
2010

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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 $O(n^{\frac{1}{3}})$ 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.