Approximation Algorithms for the Maximum Weight Internal Spanning Tree Problem

Given a vertex-weighted connected graphG = (V,E), the maximum weight internal spanning tree (MwIST for short) problem asks for a spanning tree T of G such that the total weight of the internal vertices in T is maximized. The unweighted variant, denoted as MIST, is NPhard and APX-hard, and the currently best approximation algorithm has a proven performance ratio 13/17. The currently best approximation algorithm for MwIST only has a performance ratio 1/3 − ǫ, for any ǫ > 0. In this paper, we present a simple algorithm based on a novel relationship between MwIST and the maximum weight matching, and show that it achieves a better approximation ratio of 1/2. When restricted to claw-free graphs, a special case been previously studied, we design a 7/12-approximation algorithm.