Distributed Agreement on Activity Driven Networks

TL;DR

This paper analyzes how consensus protocols behave in activity driven networks, providing bounds on convergence rates that are computationally feasible, with validation through simulations.

Contribution

It introduces new bounds for convergence rates in temporal networks that are easier to compute than existing methods.

Findings

Derived bounds for convergence rates in sparse and fast-switching networks

Validated theoretical results with numerical simulations

Provided practical methods for analyzing consensus in time-varying networks

Abstract

In this paper, we investigate asymptotic properties of a consensus protocol taking place in a class of temporal (i.e., time-varying) networks called the activity driven network. We first show that a standard methodology provides us with an estimate of the convergence rate toward the consensus, in terms of the eigenvalues of a matrix whose computational cost grows exponentially fast in the number of nodes in the network. To overcome this difficulty, we then derive alternative bounds involving the eigenvalues of a matrix that is easy to compute. Our analysis covers the regimes of 1) sparse networks and 2) fast-switching networks. We numerically confirm our theoretical results by numerical simulations.