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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 itconverges in $O(n^2)$ rounds. Thus, this algorithm improves the convergencetime of previously known self-stabilizing asynchronous MST algorithms by amultiplicative factor $\Theta(n)$, to the price of increasing the best knownspace complexity by a factor $O(\log n)$. The main ingredient used in ouralgorithm is the design, for the first time in self-stabilizing settings, of alabeling scheme for computing the nearest common ancestor with only$O(\log^2n)$ bits.

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