Abstract-Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust message-passing schemes for distributed information processing over networks. However, for many topologies that are realistic for wireless ad-hoc and sensor networks (like grids and random geometric graphs), the standard nearest-neighbor gossip converges as slowly as flooding (O(n 2 ) messages). A recently proposed algorithm called geographic gossip improves gossip efficiency by a p n factor, by exploiting geographic information to enable multihop long-distance communications. This paper proves that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional p n factor, and is order optimal (O(n) messages) for grids and random geometric graphs with high probability. We develop a general technique (travel agency method) based on Markov chain mixing time inequalities which can give bounds on the performance of randomized message-passing algorithms operating over various graph topologies.
Benezit et al. REF showed that an extension of geographic gossip that averages along the routed paths can further reduce the convergence time to O(n log n) which is optimal for random geometric graphs and grids.
Order-Optimal Consensus Through Randomized Path Averaging
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science Mathematics