Devismes, Stéphane and Ilcinkas, David and Johnen, Colette - Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps

dmtcs:4116 - Discrete Mathematics & Theoretical Computer Science, November 30, 2017, Vol 19 no. 3
Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps

Authors: Devismes, Stéphane and Ilcinkas, David and Johnen, Colette

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.


Source : oai:HAL:hal-01485652v4
Volume: Vol 19 no. 3
Section: Distributed Computing and Networking
Published on: November 30, 2017
Submitted on: August 22, 2017
Keywords: Disconnected network,Routing algorithm,Shortest path,Distributed algorithm,Self-stabilization,Shortest-path tree,[INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI]


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