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Making Self-Stabilizing Algorithms for Any Locally Greedy Problem

Authors Johanne Cohen , Laurence Pilard , Mikaël Rabie, Jonas Sénizergues

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Author Details

Johanne Cohen
  • Université Paris-Saclay, CNRS, LISN, 91405, Orsay, France
Laurence Pilard
  • LI-PaRAD, UVSQ, Université Paris-Saclay, France
Mikaël Rabie
  • IRIF-CNRS, Université Paris Cité, France
Jonas Sénizergues
  • Université Paris-Saclay, CNRS, LISN, 91405, Orsay, France

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Johanne Cohen, Laurence Pilard, Mikaël Rabie, and Jonas Sénizergues. Making Self-Stabilizing Algorithms for Any Locally Greedy Problem. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.SAND.2023.11

Abstract

Self-stabilizing algorithms are a way to deal with network dynamicity, as it will update itself after a network change (addition or removal of nodes or edges), as long as changes are not frequent. We propose an automatic transformation of synchronous distributed algorithms that solve locally greedy and mendable problems into self-stabilizing algorithms in anonymous networks.
Mendable problems are a generalization of greedy problems where any partial solution may be transformed -instead of completed- into a global solution: every time we extend the partial solution, we are allowed to change the previous partial solution up to a given distance. Locally here means that to extend a solution for a node, we need to look at a constant distance from it. 
In order to do this, we propose the first explicit self-stabilizing algorithm computing a (k,k-1)-ruling set (i.e. a "maximal independent set at distance k"). By combining this technique multiple times, we compute a distance-K coloring of the graph. With this coloring we can finally simulate Local model algorithms running in a constant number of rounds, using the colors as unique identifiers.
Our algorithms work under the Gouda daemon, similar to the probabilistic daemon: if an event should eventually happen, it will occur.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Greedy Problem
  • Ruling Set
  • Distance-K Coloring
  • Self-Stabilizing Algorithm

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