Local Interference Can Accelerate Gossip Algorithms

In this paper, we show how interference can be exploited to perform gossip computations for average-based consensus over a larger local neighborhood, rather than only pairs of nodes. We use a new channel coding technique called computation coding to compute sums reliably over the wireless medium. Since many nodes can simultaneously average in a single round, our neighborhood gossip algorithm converges faster than the standard nearest neighbor gossip algorithm. For a network with n nodes and size m neighborhoods, neighborhood gossip requires O(n²/m²) rounds while standard gossip requires Θ(n²) rounds. Furthermore, we show that if the power path loss coefficient is less than 4, the total transmit energy employed by neighborhood gossip is polynomially smaller than that employed by standard gossip.