On Distributed Averaging Algorithms and Quantization Effects

TL;DR

This paper analyzes distributed averaging algorithms over dynamic networks, providing bounds on convergence time and error, especially under quantization constraints, and introduces an optimal algorithm within this class.

Contribution

It offers tight polynomial bounds on convergence time for a broad class of averaging algorithms and introduces an optimal algorithm for time-varying topologies.

Findings

Tight polynomial bounds on convergence time for unquantized algorithms.

Error bounds and convergence time bounds under quantization.

Identification of an algorithm with the best convergence time among existing methods.

Abstract

We consider distributed iterative algorithms for the averaging problem over time-varying topologies. Our focus is on the convergence time of such algorithms when complete (unquantized) information is available, and on the degradation of performance when only quantized information is available. We study a large and natural class of averaging algorithms, which includes the vast majority of algorithms proposed to date, and provide tight polynomial bounds on their convergence time. We also describe an algorithm within this class whose convergence time is the best among currently available averaging algorithms for time-varying topologies. We then propose and analyze distributed averaging algorithms under the additional constraint that agents can only store and communicate quantized information, so that they can only converge to the average of the initial values of the agents within some error. We establish bounds on the error and tight bounds on the convergence time, as a function of the number of quantization levels.