Self-Stabilizing MIS Computation in the Beeping Model

Authors George Giakkoupis , Volker Turau , Isabella Ziccardi



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Author Details

George Giakkoupis
  • Inria, Univ Rennes, CNRS, IRISA, France
Volker Turau
  • Institute of Telematics, Hamburg University of Technology, Germany
Isabella Ziccardi
  • Bocconi University, BIDSA, Milan, Italy

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George Giakkoupis, Volker Turau, and Isabella Ziccardi. Self-Stabilizing MIS Computation in the Beeping Model. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DISC.2024.28

Abstract

We consider self-stabilizing algorithms to compute a Maximal Independent Set (MIS) in the extremely weak beeping communication model. The model consists of an anonymous network with synchronous rounds. In each round, each vertex can optionally transmit a signal to all its neighbors (beep). After the transmission of a signal, each vertex can only differentiate between no signal received, or at least one signal received. We also consider an extension of this model where vertices can transmit signals through two distinguishable beeping channels. We assume that vertices have some knowledge about the topology of the network. We revisit the not self-stabilizing algorithm proposed by Jeavons, Scott, and Xu (2013), which computes an MIS in the beeping model. We enhance this algorithm to be self-stabilizing, and explore three different variants, which differ in the knowledge about the topology available to the vertices and the number of beeping channels. In the first variant, every vertex knows an upper bound on the maximum degree Δ of the graph. For this case, we prove that the proposed self-stabilizing version maintains the same run-time as the original algorithm, i.e., it stabilizes after O(log n) rounds w.h.p. on any n-vertex graph. In the second variant, each vertex only knows an upper bound on its own degree. For this case, we prove that the algorithm stabilizes after O(log n⋅ log log n) rounds on any n-vertex graph, w.h.p. In the third variant, we consider the model with two beeping channels, where every vertex knows an upper bound of the maximum degree of the nodes in the 1-hop neighborhood. We prove that this variant stabilizes w.h.p. after O(log n) rounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Maximal Independent Set
  • Self-Stabilization
  • Beeping Model

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References

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