Geographic Gossip: Efficient Averaging for Sensor Networks

Abstract

Abstract-Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of and , respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy using ( ( 1 5 log ) log 1 ) radio transmissions, which yields a log factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.

Analysis of accelerated gossip algorithms

“…The authors of [7] introduce simple and numerically stable algorithms with better worst-case performance. In [8], a probabilistic counting mechanism is utilized to improve the convergence rate and in [9] sensors' location information is exploited to boost the convergence. Among all the proposed acceleration strategies, there is one particular approach that has motivated the research in this paper.…”

Fast Decentralized Averaging via Multi-scale Gossip

“…Our primary measure of performance is communication cost-the number of messages (transmissions over a single hop) required to compute an estimate to accuracy-which is also considered in [4,5]. In the analysis of scaling laws for gossip algorithms, a commonly studied measure of convergence rate is the averaging time, denoted T (n), which is the number of iterations required to reach an estimate with accuracy with high probability 3 .…”

“…A variant called geographic gossip, proposed by Dimakis, Sarwate, and Wainwright [5], achieves a similar communication cost of Θ( n 1.5 √ log n log −1 ) by allowing distant (non-neighbouring) pairs of nodes to gossip at each iteration. Assuming that each node knows its own coordinates and the coordinates of its neighbours in the unit square, communication between arbitrary pairs of nodes is made possible using greedy geographic routing.…”

“…If a node is closer to the target than all of its neighbours, this is the final message recipient. It is shown in [5] that for random geometric graphs with connectivity radius r(n) = r con (n), greedy geographic routing succeeds with high probability. For an alternative form of greedy geographic routing, which may be useful in implementations, see [13].…”

“…For an alternative form of greedy geographic routing, which may be useful in implementations, see [13]. The main contribution of [5] is to illustrate that allowing nodes to gossip over multiple hops can lead to significant improvements in communication cost. In follow-up work, Benezit, Dimakis, Thiran, and Vetterli [4] showed that a modified version of geographic gossip, called path averaging, can achieve Θ(n log −1 ) communication cost on random geometric graphs.…”