Fast Self-Stabilizing Minimum Spanning Tree Construction Using Compact Nearest Common Ancestor Labeling Scheme

Lélia Blin (1, 2) , Shlomi Dolev (3) , Maria Gradinariu Potop-Butucaru (2) , Stephane Rovedakis (4)

1 UEVE - Université d'Évry-Val-d'Essonne
2 NPA - Networks and Performance Analysis
3 Department of Computer Science [Beer-Sheva]
4 CEDRIC - ROC - CEDRIC. Réseaux et Objets Connectés

We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of previously known self-stabilizing asynchronous MST algorithms by a multiplicative factor $\Theta(n)$, to the price of increasing the best known space complexity by a factor $O(\log n)$. The main ingredient used in our algorithm is the design, for the first time in self-stabilizing settings, of a labeling scheme for computing the nearest common ancestor with only $O(\log^2n)$ bits.

Mots clés: Self-stabilizing algorithm; Convergence time; Labeling scheme; Minimum spanning trees; Space complexity

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Algorithme et structure de données [cs.DS]; Réseaux et télécommunications [cs.NI]

Lélia Blin, Shlomi Dolev, Maria Gradinariu Potop-Butucaru, Stephane Rovedakis. Fast Self-Stabilizing Minimum Spanning Tree Construction Using Compact Nearest Common Ancestor Labeling Scheme. [Research Report] LIP6 UMR 7606, INRIA, UPMC Sorbonne Universités, France. 2013. ⟨hal-00879578⟩