Fast Self-Stabilizing Minimum Spanning Tree Construction Using Compact Nearest Common Ancestor Labeling Scheme - Archive ouverte HAL Access content directly
Reports (Research Report) Year : 2013

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

Lélia Blin
Shlomi Dolev
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Stephane Rovedakis

#### Abstract

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.

### Dates and versions

hal-00879578 , version 1 (04-11-2013)

### Identifiers

• HAL Id : hal-00879578 , version 1
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### Cite

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⟩

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