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 all 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.