Convergence and Robustness Bounds for Distributed Asynchronous Shortest-Path

TL;DR

This paper provides convergence and robustness bounds for asynchronous distributed shortest-path algorithms, specifically analyzing the Adaptive Bellman--Ford method under asynchronous conditions and noise, extending prior synchronous results.

Contribution

It extends finite-time convergence and robustness bounds from synchronous to asynchronous shortest-path algorithms, including noise robustness analysis.

Findings

Finite-time convergence bounds for asynchronous Adaptive Bellman--Ford.

Robustness guarantees against interval-bounded noise.

Convergence guarantees for asynchronous most-probable-path algorithms.

Abstract

This work analyzes convergence times and robustness bounds for asynchronous distributed shortest-path computation. We focus on the Adaptive Bellman--Ford algorithm, a self-stabilizing method in which each agent updates its shortest-path estimate based only on the estimates of its neighbors and forgetting its previous estimate. In the asynchronous framework considered in this paper, agents are allowed to idle or encounter race conditions during their execution of the Adaptive Bellman--Ford algorithm. We build on Lyapunov-based results that develop finite-time convergence and robustness bounds for the synchronous shortest-path setting, in order to produce finite-time convergence and robustness bounds for the asynchronous setting. We also explore robustness against interval-bounded noise processes and establish convergence and robustness guarantees for asynchronous most-probable-path algorithms.