# Approximation Algorithms for the Maximum Weight Internal Spanning Tree Problem

Ontology type: schema:Chapter      Open Access: True

### Chapter Info

DATE

2017-07-01

AUTHORS ABSTRACT

Given a vertex-weighted connected graph \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G = (V, E)$$\end{document}, 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 NP-hard 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/3 - \epsilon$$\end{document}, for any \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon > 0$$\end{document}. 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. More... »

PAGES

124-136

### Book

TITLE

Computing and Combinatorics

ISBN

978-3-319-62388-7
978-3-319-62389-4

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-62389-4_11

DOI

http://dx.doi.org/10.1007/978-3-319-62389-4_11

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1090448513

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