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

  • Li-Hsuan Chen
  • Dun-Wei Cheng
  • Sun-Yuan Hsieh
  • Ling-Ju HungEmail author
  • Chia-Wei Lee
  • Bang Ye Wu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)

Abstract

Given a metric graph \(G=(V, E, w)\) and a center \(c\in V\), and an integer k, the Star k-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 Star k-Hub Center Problem is NP-hard. (Liang, Operations Research Letters, 2013) proved that for any \(\epsilon >0\), it is NP-hard to approximate the Star k-Hub Center Problem to within a ratio \(1.25-\epsilon \). In the same paper, a 3.5-approximation algorithm was given for the Star k-Hub Center Problem. In this paper, we show that for any \(\epsilon > 0\), to approximate the Star k-Hub Center Problem to a ratio \(1.5 - \epsilon \) is NP-hard. Moreover, we give 2-approximation and \(\frac{5}{3}\)-approximation algorithms for the same problem.

Keywords

Approximation Algorithm Optimization Criterion Center Problem Demand Node Integer Programming Formulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Li-Hsuan Chen
    • 1
  • Dun-Wei Cheng
    • 2
  • Sun-Yuan Hsieh
    • 2
  • Ling-Ju Hung
    • 2
    Email author
  • Chia-Wei Lee
    • 2
  • Bang Ye Wu
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityChiayiTaiwan
  2. 2.Department of Computer Science and Information EngineeringNational Cheng Kung UniversityTainanTaiwan

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