Optimization and Analysis of Distributed Averaging with Short Node Memory

In this paper, we demonstrate, both theoretically and by numerical examples, that adding a local prediction component to the update rule can significantly improve the convergence rate of distributed averaging algorithms. We focus on the case where the local predictor is a linear combination of the node's two previous values (i.e., two memory taps), and our update rule computes a combination of the predictor and the usual weighted linear combination of values received from neighbouring nodes. We derive the optimal mixing parameter for combining the predictor with the neighbors' values, and carry out a theoretical analysis of the improvement in convergence rate that can be obtained using this acceleration methodology. For a chain topology on n nodes, this leads to a factor of n improvement over the one-step algorithm, and for a two-dimensional grid, our approach achieves a factor of n^1/2 improvement, in terms of the number of iterations required to reach a prescribed level of accuracy

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Consensus Propagation

We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better scaling properties than pairwise averaging, an alternative that has received much recent attention. Consensus propagation can be viewed as a special case of belief propagation, and our results contribute to the belief propagation literature. In particular, beyond singly-connected graphs, there are very few classes of relevant problems for which belief propagation is known to converge.Comment: journal versio