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

  • Ajoy K. Datta
  • Stéphane DevismesEmail author
  • Colette Johnen
  • Lawrence L. Larmore
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11914)

Abstract

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 \(\varTheta (1)\) 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 \(O({\mathcal {D}}\cdot n^2)\) rounds, where \({\mathcal {D}}\) is the network diameter and n the number of processes.

Keywords

Self-stabilization BFS spanning tree Distributed unfair daemon Stabilization time Round complexity 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ajoy K. Datta
    • 1
  • Stéphane Devismes
    • 2
    Email author
  • Colette Johnen
    • 3
  • Lawrence L. Larmore
    • 1
  1. 1.Department of Computer ScienceUniversity of NevadaRenoUSA
  2. 2.Université Grenoble Alpes, VERIMAG, UMR 5104GrenobleFrance
  3. 3.Université de Bordeaux, LaBRI, UMR 5800BordeauxFrance

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