Constructing Stochastic Matrices for Weighted Averaging in Gossip Networks

TL;DR

This paper introduces an algorithm to construct stochastic matrices for gossip networks that guarantee convergence to a weighted average, addressing a less-explored aspect of consensus algorithms.

Contribution

The work presents a novel method for generating stochastic matrices tailored to network topology and weights, ensuring finite convergence in gossip processes.

Findings

Algorithm guarantees convergence to a weighted consensus.

Applicable to various network topologies and weight configurations.

Ensures finite-time convergence to a rank-one matrix.

Abstract

The convergence of the gossip process has been extensively studied; however, algorithms that generate a set of stochastic matrices, the infinite product of which converges to a rank-one matrix determined by a given weight vector, have been less explored. In this work, we propose an algorithm for constructing (local) stochastic matrices based on a given gossip network topology and a set of weights for averaging across different consensus clusters, ensuring that the gossip process converges to a finite limit set.