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Self-stabilization and Byzantine Tolerance for Maximal Matching

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Stabilization, Safety, and Security of Distributed Systems (SSS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11201))

Abstract

We analyse the impact of transient and Byzantine faults on the construction of a maximal matching in a general network. We consider the self-stabilizing algorithm called AnonyMatch presented by Cohen et al. [3] for computing such a matching. Since self-stabilization is transient fault tolerant, we prove that this algorithm still works under the more difficult context of arbitrary Byzantine faults. Byzantine nodes can prevent nodes close to them from taking part in the matching for an arbitrarily long time. We give bounds on their impact depending on the distance between a non-Byzantine node and the closest Byzantine, called the containment radius. We present the first algorithm tolerating both transient and Byzantine faults under the fair distributed daemon while keeping the best known containment radius. We prove this algorithm converges in \(O(\max (\varDelta n, \varDelta ^2 \log n))\) rounds w.h.p., where n and \(\varDelta \) are the size and the maximum degree of the network, resp.. Additionally, we improve the best known complexity as well as the best containment radius for this problem under the fair central daemon.

S. Kunne—This work is eligible for best student paper.

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Notes

  1. 1.

    A matching M is 1-maximal if it is not possible to build a matching by removing one edge and adding two edges to M.

  2. 2.

    Alternatively, the daemon could specify a set of pairs (enabled node, rule for which that node is enabled). In our algorithm, all guards are mutually exclusive; that is, at any time, a given node can be enabled for one rule at most. Therefore, that distinction does not matter.

  3. 3.

    The names and definitions of the six classes are inspired by similar definitions in [3, 8], but were adapted to form a partition and to depend on the states of node u and its direct neighbours’ internal variables only.

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Authors and Affiliations

  1. LRI-CNRS, Université Paris-Sud, Université Paris Saclay, Orsay, France

    Stephan Kunne & Johanne Cohen

  2. LI-PaRAD, Université Versailles-St. Quentin, Université Paris Saclay, Versailles, France

    Laurence Pilard

Authors
  1. Stephan Kunne
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  2. Johanne Cohen
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  3. Laurence Pilard
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Corresponding author

Correspondence to Johanne Cohen .

Editor information

Editors and Affiliations

  1. Nagoya Institute of Technology, Nagoya, Japan

    Taisuke Izumi

  2. Telecom ParisTech, Paris, France

    Petr Kuznetsov

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Kunne, S., Cohen, J., Pilard, L. (2018). Self-stabilization and Byzantine Tolerance for Maximal Matching. In: Izumi, T., Kuznetsov, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2018. Lecture Notes in Computer Science(), vol 11201. Springer, Cham. https://doi.org/10.1007/978-3-030-03232-6_6

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  • DOI: https://doi.org/10.1007/978-3-030-03232-6_6

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  • Online ISBN: 978-3-030-03232-6

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