Self-stabilization with path algebra

  • Authors:
  • Bertrand Ducourthial;Sébastien Tixeuil

  • Affiliations:
  • Laboratoire HEUDIASYC, UMR CNRS 6599, Université de Technologie de Compiègne, 60205 Compiègne Cedex, France;Laboratoire de Recherche en Informatique, UMR CNRS 8623, Université de Paris-Sud, 91405 Orsay Cedex, France

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

Self-stabilizing protocols can resist transient failures and guarantee system recovery in a finite time. We highlight the connexion between the formalism of self-stabilizing distributed systems and the formalism of generalized path algebra and asynchronous iterations with delay. We use the later to prove that a local condition on locally executed algorithm (being a strictly idempotent r-operator) ensures self-stabilization of the global system. As a result, a parametrized distributed algorithm applicable to any directed graph topology is proposed, and the function parameter of our algorithm is instantiated to produce distributed algorithms for both fundamental and high-level applications. Due to fault resilience properties of our algorithm, the resulting protocols are self-stabilizing at no additional cost.