Greedy Gossip with Eavesdropping

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.

💡 Research Summary

The paper introduces Greedy Gossip with Eavesdropping (GGE), a novel randomized gossip algorithm designed for distributed average‑consensus in wireless networks. Traditional randomized gossip selects a neighbor uniformly at random for each update, which is simple but often converges slowly, especially in large or sparsely connected graphs. Geographic gossip accelerates convergence by exploiting node locations, yet it requires costly position information and routing. GGE bridges this gap by leveraging the broadcast nature of wireless communication: every transmission is heard by all one‑hop neighbors, allowing each node to maintain an up‑to‑date local copy of its neighbors’ current values through passive eavesdropping.

When a node’s local timer fires, it does not pick a random neighbor. Instead, it scans its stored neighbor values and selects the neighbor whose value differs most from its own. The two nodes then exchange their values via a broadcast and both replace their states with the arithmetic mean of the two values. Because the broadcast is heard by all surrounding nodes, the updated values are instantly available to other neighbors without additional control messages.

The authors prove that GGE converges to the exact average for any connected undirected graph. The proof models the state vector x(k) as evolving under a random, symmetric, doubly‑stochastic matrix W_k that depends on the selected pair at iteration k. By relating the expected squared error E