Distributed Computation of Mixing Time

TL;DR

This paper introduces a scalable distributed algorithm for efficiently estimating the mixing time of undirected graphs using random walks, suitable for networks with bandwidth limitations.

Contribution

It presents the first lightweight distributed algorithm that estimates mixing time in $O( au_s \, \log n)$ rounds within the CONGEST model.

Findings

Estimates mixing time with $O( au_s \log n)$ rounds.

Uses minimal memory and local computation.

Operates efficiently under bandwidth constraints.

Abstract

The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We present an efficient distributed algorithm for computing the mixing time of undirected graphs. Our algorithm estimates the mixing time $\tau_s$ (with respect to a source node $s$) of any $n$-node undirected graph in $O(\tau_s \log n)$ rounds. Our algorithm is based on random walks and require very little memory and use lightweight local computations, and work in the CONGEST model. Hence our algorithm is scalable under bandwidth constraints and can be an helpful building block in the design of topologically aware networks.