Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps

Abstract : We deal with the problem of maintaining a shortest-path tree rooted at some process r in a network that may be disconnected after topological changes. The goal is then to maintain a shortest-path tree rooted at r in its connected component, V_r, and make all processes of other components detecting that r is not part of their connected component. We propose, in the composite atomicity model, a silent self-stabilizing algorithm for this problem working in semi-anonymous networks, where edges have strictly positive weights. This algorithm does not require any a priori knowledge about global parameters of the network. We prove its correctness assuming the distributed unfair daemon, the most general daemon. Its stabilization time in rounds is at most 3nmax+D, where nmax is the maximum number of non-root processes in a connected component and D is the hop-diameter of V_r. Furthermore, if we additionally assume that edge weights are positive integers, then it stabilizes in a polynomial number of steps: namely, we exhibit a bound in O(maxi nmax^3 n), where maxi is the maximum weight of an edge and n is the number of processes.
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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2017, Vol 19 no. 3, pp.14 - 14
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Soumis le : jeudi 30 novembre 2017 - 11:03:47
Dernière modification le : vendredi 6 juillet 2018 - 10:08:02

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  • HAL Id : hal-01485652, version 4
  • ARXIV : 1703.03315

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Stéphane Devismes, David Ilcinkas, Colette Johnen. Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2017, Vol 19 no. 3, pp.14 - 14. 〈hal-01485652v4〉

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