Brief Announcement: Analysis of a Memory-Efficient Self-stabilizing BFS Spanning Tree Construction

Lawrence Larmore, University of Nevada, Las Vegas
Ajoy Datta, University of Nevada, Las Vegas
Stéphane Devismes, Université Grenoble Alpes
Colette Johnen, Université de Bordeaux


We present preliminary results on the last topic we collaborate with our late friend, Professor Ajoy Kumar Datta (1958–2019), who prematurely left us a few months ago. In this work, we shed new light on a self-stabilizing wave algorithm proposed by Colette Johnen in 1997 [12]. This algorithm constructs a BFS spanning tree in any connected rooted network. Nowadays, it is still the best existing self-stabilizing BFS spanning tree construction in terms of memory requirement, i.e., it only requires Θ(1) bits per edge. However, it has been proven assuming a weakly fair daemon. Moreover, its stabilization time was unknown. Here, we study the slightly modified version of this algorithm, still keeping the same memory requirement. We prove the self-stabilization of this variant under the distributed unfair daemon and show a stabilization time in O(D⋅n2) rounds, where D is the network diameter and n the number of processes.