Convergence Time of Quantized Metropolis Consensus Over Time-Varying Networks

TL;DR

This paper analyzes the convergence time of a quantized consensus protocol over dynamic networks, showing it reaches consensus efficiently with an expected time of O(n^2 log^2 n) under certain stochastic activation conditions.

Contribution

It introduces a fast-converging quantized consensus protocol for time-varying networks with provable bounds on convergence time.

Findings

Expected convergence time is at most O(n^2 log^2 n)

Protocol achieves consensus with a constant number of updates per node

Applicable to networks with Poisson-activated edges

Abstract

We consider the quantized consensus problem on undirected time-varying connected graphs with n nodes, and devise a protocol with fast convergence time to the set of consensus points. Specifically, we show that when the edges of each network in a sequence of connected time-varying networks are activated based on Poisson processes with Metropolis rates, the expected convergence time to the set of consensus points is at most O(n^2 log^2 n), where each node performs a constant number of updates per unit time.