Multi-hop Greedy Gossip with Eavesdropping

Greedy gossip with eavesdropping (GGE) is a randomized gossip algorithm that computes the average consensus by exploiting the broadcast nature of wireless communications. Each node eavesdrops on its immediate neighbors to track their values so that when it comes time to gossip, a node can myopically exchange information with the neighbor that will give the greatest immediate improvement in local squared error. In previous work, we showed that the improvement achieved using GGE over standard randomized gossip (i.e., exchanging information equally often with all neighbors) is proportional to the maximum node degree. Thus, for network topologies such as random geometric graphs, where node degree grows with the network size, the improvements of GGE scale with network size, but for grid-like topologies, where the node degree remains constant, GGE yields limited improvement. This paper presents an extension to GGE, which we call ldquomulti-hop GGErdquo, that improves the rate of convergence for grid-like topologies. Multi-hop GGE relies on artificially increasing neighborhood size by performing greedy updates with nodes beyond one hop neighborhoods. We show that multi-hop GGE converges to the average consensus and illustrate via simulation that multi-hop GGE improves the performance of GGE for different network topologies.