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The Mixed Center Location Problem

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Combinatorial Optimization and Applications (COCOA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10043))

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Abstract

This paper studies a new version of the location problem called the mixed center location problem. Let P be a set of n points in the plane. We first consider the mixed 2-center problem where one of the centers must be in P and solve it in \(O(n^2\log n)\) time. Next we consider the mixed k-center problem where m of the centers are in P. Motivated by two practical constraints, we propose two variations of the problem. We present an exact algorithm, a 2-approximation algorithm and a heuristic algorithm solving the mixed k-center problem. The time complexity of the exact algorithm is \(O(n^{m+O(\sqrt{k-m})})\).

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Yi Xu & Jigen Peng

  2. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048, People’s Republic of China

    Jigen Peng

  3. School of Management, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Yinfeng Xu

  4. The State Key Lab for Manufacturing Systems Engineering, Xi’an, 710049, People’s Republic of China

    Yinfeng Xu

Authors
  1. Yi Xu
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  2. Jigen Peng
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  3. Yinfeng Xu
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Corresponding author

Correspondence to Yi Xu .

Editor information

Editors and Affiliations

  1. University of Hong Kong, Hong Kong, China

    T-H. Hubert Chan

  2. City University of Hong Kong, Hong Kong, China

    Minming Li

  3. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

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© 2016 Springer International Publishing AG

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Xu, Y., Peng, J., Xu, Y. (2016). The Mixed Center Location Problem. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_25

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  • DOI: https://doi.org/10.1007/978-3-319-48749-6_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48748-9

  • Online ISBN: 978-3-319-48749-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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