Greedy Gossip with Eavesdropping

TL;DR

This paper introduces greedy gossip with eavesdropping (GGE), a decentralized wireless algorithm that rapidly computes average consensus by greedily selecting neighbors with the most different values, leveraging broadcast eavesdropping.

Contribution

The paper proposes GGE, a novel gossip algorithm that uses greedy neighbor selection based on eavesdropped information, improving convergence speed without requiring location data.

Findings

GGE guarantees convergence on connected networks.

GGE outperforms randomized gossip in convergence rate.

GGE performs comparably to geographic gossip in simulations.

Abstract

This paper presents greedy gossip with eavesdropping (GGE), a novel randomized gossip algorithm for distributed computation of the average consensus problem. In gossip algorithms, nodes in the network randomly communicate with their neighbors and exchange information iteratively. The algorithms are simple and decentralized, making them attractive for wireless network applications. In general, gossip algorithms are robust to unreliable wireless conditions and time varying network topologies. In this paper we introduce GGE and demonstrate that greedy updates lead to rapid convergence. We do not require nodes to have any location information. Instead, greedy updates are made possible by exploiting the broadcast nature of wireless communications. During the operation of GGE, when a node decides to gossip, instead of choosing one of its neighbors at random, it makes a greedy selection, choosing the node which has the value most different from its own. In order to make this selection, nodes need to know their neighbors' values. Therefore, we assume that all transmissions are wireless broadcasts and nodes keep track of their neighbors' values by eavesdropping on their communications. We show that the convergence of GGE is guaranteed for connected network topologies. We also study the rates of convergence and illustrate, through theoretical bounds and numerical simulations, that GGE consistently outperforms randomized gossip and performs comparably to geographic gossip on moderate-sized random geometric graph topologies.