Title

Analysis of a Memory-Efficient Self-Stabilizing BFS Spanning Tree

Document Type

Article

Publication Date

7-18-2019

Publication Title

Computing Research Repository

Publisher

Cornell University

First page number:

1

Last page number:

40

Abstract

We present results on the last topic we collaborate with our late friend, Professor Ajoy Kumar Datta (1958-2019). In this work, we shed new light on a self-stabilizing wave algorithm proposed by Colette Johnen in 1997. 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, {\em 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.

Keywords

Self-Stabilization; BFS Spanning Tree; Distributed Unfair Daemon; Stabilization Time; Round Complexity

Disciplines

Computer Sciences | Physical Sciences and Mathematics

Language

English


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