Approximation Algorithms for the Star k-Hub Center Problem in Metric Graphs

Ontology type: schema:Chapter

Chapter Info

DATE

2016-07-20

AUTHORS ABSTRACT

Given a metric graph \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G=(V, E, w)$$\end{document} and a center \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c\in V$$\end{document}, and an integer k, the Stark-Hub Center Problem is to find a depth-2 spanning tree T of G rooted by c such that c has exactly k children and the diameter of T is minimized. Those children of c in T are called hubs. The Stark-Hub Center Problem is NP-hard. (Liang, Operations Research Letters, 2013) proved that 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}, it is NP-hard to approximate the Stark-Hub Center Problem to within a ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.25-\epsilon$$\end{document}. In the same paper, a 3.5-approximation algorithm was given for the Stark-Hub Center Problem. In this paper, we show that 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}, to approximate the Stark-Hub Center Problem to a ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.5 - \epsilon$$\end{document} is NP-hard. Moreover, we give 2-approximation and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{5}{3}$$\end{document}-approximation algorithms for the same problem. More... »

PAGES

222-234

Book

TITLE

Computing and Combinatorics

ISBN

978-3-319-42633-4
978-3-319-42634-1

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-42634-1_18

DOI

http://dx.doi.org/10.1007/978-3-319-42634-1_18

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1017593052

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