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Compact deterministic self-stabilizing leader election on a ring: the exponential advantage of being talkative

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Abstract

This paper focuses on compact deterministic self-stabilizing solutions for the leader election problem. When the solution is required to be silent (i.e., when the state of each process remains fixed from some point in time during any execution), there exists a lower bound of \(\varOmega (\log n)\) bits of memory per participating node , where n denotes the number of nodes in the system. This lower bound holds even in rings. We present a new deterministic (non-silent) self-stabilizing protocol for n-node rings that uses only \(O(\log \log n)\) memory bits per node, and stabilizes in \(O(n\log ^2 n)\) rounds. Our protocol has several attractive features that make it suitable for practical purposes. First, it assumes an execution model that is used by existing compilers for real networks. Second, the size of the ring (or any upper bound on this size) does not need to be known by any node. Third, the node identifiers can be of various sizes. Finally, no synchrony assumption, besides weak fairness, is assumed. Our result shows that, perhaps surprisingly, silence can be traded for an exponential decrease in memory space without significantly increasing stabilization time or introducing restrictive assumptions.

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Authors and Affiliations

  1. Université d’Evry-Val d’Essonne, 91000, Evry, France

    Lélia Blin

  2. UPMC Sorbonne Universités, Paris, France

    Lélia Blin & Sébastien Tixeuil

  3. LIP6-CNRS UMR 7606, Paris, France

    Lélia Blin & Sébastien Tixeuil

  4. Institut Universitaire de France, Paris, France

    Sébastien Tixeuil

Authors
  1. Lélia Blin
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  2. Sébastien Tixeuil
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Correspondence to Lélia Blin.

Additional information

Lélia Blin: Additional support from the ANR project IRIS.

A preliminary version of this paper has appeared in [12, 13].

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Blin, L., Tixeuil, S. Compact deterministic self-stabilizing leader election on a ring: the exponential advantage of being talkative. Distrib. Comput. 31, 139–166 (2018). https://doi.org/10.1007/s00446-017-0294-2

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