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Approximation Algorithm for Cycle-Star Hub Network Design Problems and Cycle-Metric Labeling Problems

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WALCOM: Algorithms and Computation (WALCOM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10167))

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Abstract

We consider a single allocation hub-and-spoke network design problem which allocates each non-hub node to exactly one of given hub nodes so as to minimize the total transportation cost. This paper deals with a case in which the hubs are located in a cycle, which is called a cycle-star hub network design problem. The problem is essentially equivalent to a cycle-metric labeling problem. The problem is useful in the design of networks in telecommunications and airline transportation systems. We propose a \(2(1-1/h)\)-approximation algorithm where h denotes the number of hub nodes. Our algorithm solves a linear relaxation problem and employs a dependent rounding procedure. We analyze our algorithm by approximating a given cycle-metric matrix by a convex combination of Monge matrices.

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Authors and Affiliations

  1. Department of Industrial Engineering and Economics, Graduate School of Engineering, Tokyo Institute of Technology, Tokyo, Japan

    Yuko Kuroki & Tomomi Matsui

Authors
  1. Yuko Kuroki
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  2. Tomomi Matsui
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Corresponding authors

Correspondence to Yuko Kuroki or Tomomi Matsui .

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Editors and Affiliations

  1. Universiti Teknologi Brunei, Bandar Seri Begawan, Brunei Darussalam

    Sheung-Hung Poon

  2. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Md. Saidur Rahman

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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Kuroki, Y., Matsui, T. (2017). Approximation Algorithm for Cycle-Star Hub Network Design Problems and Cycle-Metric Labeling Problems. In: Poon, SH., Rahman, M., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2017. Lecture Notes in Computer Science(), vol 10167. Springer, Cham. https://doi.org/10.1007/978-3-319-53925-6_31

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  • DOI: https://doi.org/10.1007/978-3-319-53925-6_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53924-9

  • Online ISBN: 978-3-319-53925-6

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