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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2017

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

Stéphane Devismes

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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Dates and versions

hal-01485652 , version 1 (09-03-2017)
hal-01485652 , version 2 (16-08-2017)
hal-01485652 , version 3 (21-08-2017)
hal-01485652 , version 4 (30-11-2017)

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Cite

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, 2017, Vol. 19 no. 3, pp.14 - 14. ⟨10.23638/DMTCS-19-3-14⟩. ⟨hal-01485652v4⟩
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