Silent self-stabilizing BFS tree algorithms revisited

• We show that the bounded-memory version of the Dolev et al’s BFS is round-optimal.
• We show that the stabilization time of the Huang and Chen’s BFS is Omega(n) rounds.
• We show that these two algorithms have exponential stabilization times in steps.

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).