Analyzing the Fault-Containment Time of Self-Stabilizing Algorithms - A Case Study for Graph Coloring

TL;DR

This paper introduces techniques to analyze fault containment times in self-stabilizing algorithms, providing bounds on recovery time and variance, with specific results for graph coloring and bounded-independence graphs.

Contribution

It offers new analytical methods to bound mean recovery time and variance for self-stabilizing algorithms, including a novel Delta+1-coloring algorithm.

Findings

Mean recovery time is bounded analytically.

Variance of recovery time is bounded by a small constant.

Containment metrics are constant for bounded-independence graphs.

Abstract

The paper presents techniques to derive upper bounds for the mean time to recover from a single fault for self-stabilizing algorithms in the message passing model. For a new Delta+1-coloring algorithm we analytically derive a bound for the mean time to recover and show that the variance is bounded by a small constant independent of the network's size. For the class of bounded-independence graphs (e.g. unit disc graphs) all containment metrics are in O(1).