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)


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.


Approximation Algorithm Optimization Criterion Center Problem Demand Node Integer Programming Formulation 
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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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