Silent Self-stabilizing BFS Tree Algorithms Revised

TL;DR

This paper revisits and refines two foundational silent self-stabilizing BFS tree algorithms, providing new adaptations and a comprehensive analysis of their correctness and stabilization complexity.

Contribution

It introduces three new adaptations of existing algorithms within the composite atomicity model and thoroughly analyzes their correctness and stabilization time.

Findings

Algorithms converge under unfair daemon assumptions.

Stabilization times are characterized in rounds and steps.

The adaptations improve understanding of self-stabilizing BFS trees.

Abstract

In this paper, we revisit two fundamental results of the self-stabilizing literature about silent BFS spanning tree constructions: the Dolev et al algorithm and the Huang and Chen's algorithm. More precisely, we propose in the composite atomicity model three straightforward adaptations inspired from those algorithms. We then present a deep study of these three algorithms. Our results are related to both correctness (convergence and closure, assuming a distributed unfair daemon) and complexity (analysis of the stabilization time in terms of rounds and steps).