Convergence speed of unsteady distributed consensus: decay estimate along the settling spanning-trees

TL;DR

This paper provides estimates for the convergence speed of non-stationary distributed consensus algorithms by analyzing information propagation along spanning trees, with results that are tight in various cases.

Contribution

It introduces a method to estimate convergence rates based on topological and quantitative information, focusing on propagation along spanning trees in communication graphs.

Findings

Results are tight in multiple instances.

Estimates are based on propagation along spanning trees.

Illustrated with simple and complex examples.

Abstract

Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries). The results appear to be tight in a number of instances and are illustrated through simple as well as more sophisticated examples. The main idea is to follow propagation of information along certain spanning trees which arise in the communication graph.