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

TL;DR

This paper introduces a new self-stabilizing algorithm for constructing minimum spanning trees that significantly improves convergence time using a compact nearest common ancestor labeling scheme, with a trade-off in space complexity.

Contribution

The paper presents the first self-stabilizing MST algorithm utilizing a compact nearest common ancestor labeling scheme, reducing convergence time.

Findings

Converges in O(n^2) rounds, faster than previous algorithms.

Uses only O(log^2 n) bits of space for labeling.

Achieves a multiplicative improvement in convergence time.

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.