A Self-Stabilizing 3-Approximation for the Maximum Leaf Spanning Tree Problem in Arbitrary Networks

Abstract. The maximum leaf spanning tree (MLST) is a good candidate for con-structing a virtual backbone in self-organized multihop wireless networks, but is practically intractable (NP-complete). Self-stabilization is a general technique that permits to recover from catastrophic transient failures in self-organized net-works without human intervention. We propose a fully distributed self-stabilizing approximation algorithm for the MLST problem on arbitrary topology networks. Our algorithm is the first self-stabilizing protocol that is specifically designed for the construction of an MLST. It improves other previous self-stabilizing solutions both for generality (arbitrary topology graphs vs. unit disk graphs or generalized unit disk graphs, respectively) and for approximation ratio, as it guarantees the number of its leaves is at least 1/3 of the maximum one. The time complexity of our algorithm is O(n2) rounds.