Self-stabilization with Path Algebra

Bertrand Ducourthial (1) , Sébastien Tixeuil (2)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
2 LRI - Laboratoire de Recherche en Informatique

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 generalised 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.

Mots clés: r-operators; self-stabilization; distributed algorithms; path algebra

Domaines: Algorithme et structure de données [cs.DS]; Calcul parallèle, distribué et partagé [cs.DC]; Réseaux et télécommunications [cs.NI]

Bertrand Ducourthial, Sébastien Tixeuil. Self-stabilization with Path Algebra. Theoretical Computer Science, 2003, 293 (1), pp.219-236. ⟨10.1016/S0304-3975(02)00238-4⟩. ⟨hal-00632374⟩