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 (Formula presented) 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 (Formula presented) rounds, where (Formula presented) is the network diameter and n the number of processes.
CITATION STYLE
Datta, A. K., Devismes, S., Johnen, C., & Larmore, L. L. (2019). And: Analysis of a Memory-Efficient Self-stabilizing BFS Spanning Tree Construction. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11914 LNCS, pp. 99–104). Springer. https://doi.org/10.1007/978-3-030-34992-9_8
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