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

Stéphane Devismes (1) , David Ilcinkas (2) , Colette Johnen (2)

1 SYNCHRONE
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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 {\em 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 $O(\texttt{W}_{\max} {n_{\texttt{maxCC}}}^3 n)$, where $\texttt{W}_{\max}$ is the maximum weight of an edge, ${n_{\texttt{maxCC}}}$ 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~$3{n_{\texttt{maxCC}}}+D$, where $D$ is the hop-diameter of $V_r$.

Mots clés: Distributed algorithm; self-stabilization; routing algorithm; shortest path; disconnected network; shortest-path tree

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Stéphane Devismes, David Ilcinkas, Colette Johnen. Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps. 20th International Conference on Principles of Distributed Systems (OPODIS 2016), Dec 2016, Madrid, Spain. pp.10:1-10:16, ⟨10.4230/LIPIcs.OPODIS.2016.10⟩. ⟨hal-01544581⟩