Abstract
In this paper, we present the last work we collaborated with our late friend, Professor Ajoy Kumar Datta (1958-2019), who prematurely left us four years ago. This article is therefore dedicated to him.In this work, we shed new light on a self-stabilizing wave algorithm proposed by Colette Johnen in 1997 [1]. Starting from an arbitrary configuration, this algorithm endlessly re-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 originally proven assuming a weakly fair daemon. Moreover, its stabilization time was unknown until now.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.
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