Gossip consensus algorithms via quantized communication

This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise ''gossip'' communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature: whether the agents should encode their communication by a deterministic or a randomized quantizer, and whether they should use, and how, exact information regarding their own states in the update.Comment: Accepted for publicatio

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

Fast Discrete Consensus Based on Gossip for Makespan Minimization in Networked Systems

In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons

An Upper Bound on the Convergence Time for Quantized Consensus of Arbitrary Static Graphs

We analyze a class of distributed quantized consensus algorithms for arbitrary static networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and then update their estimation by communicating with their neighbors in a limited capacity channel in an asynchronous clock setting. Eventually, all nodes reach consensus with quantized precision. We analyze the expected convergence time for the general quantized consensus algorithm proposed by Kashyap et al \cite{Kashyap}. We use the theory of electric networks, random walks, and couplings of Markov chains to derive an $O(N^3\log N)$ upper bound for the expected convergence time on an arbitrary graph of size $N$, improving on the state of art bound of $O(N^5)$ for quantized consensus algorithms. Our result is not dependent on graph topology. Example of complete graphs is given to show how to extend the analysis to graphs of given topology.Comment: to appear in IEEE Trans. on Automatic Control, January, 2015. arXiv admin note: substantial text overlap with arXiv:1208.078

Design and Analysis of Distributed Averaging with Quantized Communication

Consider a network whose nodes have some initial values, and it is desired to design an algorithm that builds on neighbor to neighbor interactions with the ultimate goal of convergence to the average of all initial node values or to some value close to that average. Such an algorithm is called generically "distributed averaging," and our goal in this paper is to study the performance of a subclass of deterministic distributed averaging algorithms where the information exchange between neighboring nodes (agents) is subject to uniform quantization. With such quantization, convergence to the precise average cannot be achieved in general, but the convergence would be to some value close to it, called quantized consensus. Using Lyapunov stability analysis, we characterize the convergence properties of the resulting nonlinear quantized system. We show that in finite time and depending on initial conditions, the algorithm will either cause all agents to reach a quantized consensus where the consensus value is the largest quantized value not greater than the average of their initial values, or will lead all variables to cycle in a small neighborhood around the average. In the latter case, we identify tight bounds for the size of the neighborhood and we further show that the error can be made arbitrarily small by adjusting the algorithm's parameters in a distributed manner