A Simple 2-Approximation for Maximum-Leaf Spanning Tree

Abstract

For an [Formula: see text]-edge connected simple graph [Formula: see text], finding a spanning tree of [Formula: see text] with the maximum number of leaves is MAXSNP-complete. The problem remains NP-complete even if [Formula: see text] is planar and the maximal degree of [Formula: see text] is at most four. Lu and Ravi gave the first known polynomial-time approximation algorithms with approximation factors [Formula: see text] and [Formula: see text]. Later, they obtained a [Formula: see text]-approximation algorithm that runs in near-linear time. The best known result is Solis-Oba, Bonsma, and Lowski’s [Formula: see text]-time [Formula: see text]-approximation algorithm. We show an alternative simple [Formula: see text]-time [Formula: see text]-approximation algorithm whose analysis is simpler. This paper is dedicated to the cherished memory of our dear friend, Professor Takao Nishizeki.