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

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## Cite As

Stéphane Devismes, David Ilcinkas, and Colette Johnen. Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.OPODIS.2016.10

## 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 under the distributed unfair daemon (the most general daemon) without requiring any a priori knowledge about global parameters of the network. This is the first algorithm for this problem that is proven to achieve a polynomial stabilization time in steps. Namely, we exhibit a bound in O(W_{max} * n_{maxCC}^3 * n), where W_{max} is the maximum weight of an edge, n_{maxCC} is the maximum number of non-root processes in a connected component, and n is the number of processes. The stabilization time in rounds is at most 3n_{maxCC} + D, where D is the hop-diameter of V_r.
##### Keywords
• distributed algorithm
• self-stabilization
• routing algorithm
• shortest path
• disconnected network
• shortest-path tree

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## References

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