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Being Efficient in Time, Space, and Workload: a Self-Stabilizing Unison and Its Consequences

Authors Stéphane Devismes , David Ilcinkas , Colette Johnen , Frédéric Mazoit

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LIPIcs.STACS.2025.30.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Distributed algorithms
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Self-stabilization
  • unison
  • time complexity
  • synchronizer

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Abstract

We present a self-stabilizing algorithm for the unison problem which is efficient in time, workload, and space in a weak model. Precisely, our algorithm is defined in the atomic-state model and works in anonymous asynchronous connected networks in which even local ports are unlabeled. It makes no assumption on the daemon and thus stabilizes under the weakest one: the distributed unfair daemon.
In an n-node network of diameter D and assuming the knowledge B ≥ 2D+2, our algorithm only requires Θ(log(B)) bits per node and is fully polynomial as it stabilizes in at most 2D+2 rounds and O(min(n²B, n³)) moves. In particular, it is the first self-stabilizing unison for arbitrary asynchronous anonymous networks achieving an asymptotically optimal stabilization time in rounds using a bounded memory at each node.
Furthermore, we show that our solution can be used to efficiently simulate synchronous self-stabilizing algorithms in asynchronous environments. For example, this simulation allows us to design a new state-of-the-art algorithm solving both the leader election and the BFS (Breadth-First Search) spanning tree construction in any identified connected network which, to the best of our knowledge, beats all existing solutions in the literature.

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Stéphane Devismes, David Ilcinkas, Colette Johnen, and Frédéric Mazoit. Being Efficient in Time, Space, and Workload: a Self-Stabilizing Unison and Its Consequences. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.30

Author Details

Stéphane Devismes
  • Laboratoire MIS, Université de Picardie, 33 rue Saint Leu - 80039 Amiens cedex 1, France
David Ilcinkas
  • Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400 Talence, France
Colette Johnen
  • Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400 Talence, France
Frédéric Mazoit
  • Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400 Talence, France

Funding

David Ilcinkas, Colette Johnen, and Frédéric Mazoit: This work was supported by the ANR project ENEDISC (ANR-24-CE48-7768). Colette Johnen and Stéphane Devismes: This work was supported by the ANR project SkyData (ANR-22-CE25-0008).

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