Broadcast gossip averaging algorithms: interference and asymptotical error in large networks

TL;DR

This paper analyzes two randomized distributed averaging algorithms, focusing on their convergence rates and errors in large networks, highlighting how network topology influences performance.

Contribution

It introduces a novel de-synchronized broadcast algorithm affected by interference and evaluates its performance compared to existing methods.

Findings

Fully-connected graphs have bounded convergence rate and error.

Locally-connected graphs achieve asymptotic accuracy as network size grows.

Interference impacts the convergence and accuracy in large networks.

Abstract

In this paper we study two related iterative randomized algorithms for distributed computation of averages. The first one is the recently proposed Broadcast Gossip Algorithm, in which at each iteration one randomly selected node broadcasts its own state to its neighbors. The second algorithm is a novel de-synchronized version of the previous one, in which at each iteration every node is allowed to broadcast, with a given probability: hence this algorithm is affected by interference among messages. Both algorithms are proved to converge, and their performance is evaluated in terms of rate of convergence and asymptotical error: focusing on the behavior for large networks, we highlight the role of topology and design parameters on the performance. Namely, we show that on fully-connected graphs the rate is bounded away from one, whereas the asymptotical error is bounded away from zero. On the contrary, on a wide class of locally-connected graphs, the rate goes to one and the asymptotical error goes to zero, as the size of the network grows larger.