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The mixed center location problem

Author

Listed:
  • Yi Xu

    (Xi’an Jiaotong University)

  • Jigen Peng

    (Xi’an Jiaotong University
    Beijing Center for Mathematics and Information Interdisciplinary Sciences)

  • Yinfeng Xu

    (Xi’an Jiaotong University
    The State Key Lab for Manufacturing Systems Engineering)

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 we solve it in $$O(n^2\log n)$$ O ( n 2 log n ) time. Second, we consider the mixed k-center problem, where m of the centers are in P, and we solve it in $$O(n^{m+O(\sqrt{k-m})})$$ O ( n m + O ( k - m ) ) time. Motivated by two practical constraints, we propose two variations of the problem. Third, we present a 2-approximation algorithm and three heuristics solving the mixed k-center problem ( $$k>2$$ k > 2 ).

Suggested Citation

  • Yi Xu & Jigen Peng & Yinfeng Xu, 2018. "The mixed center location problem," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1128-1144, November.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:4:d:10.1007_s10878-017-0183-4
    DOI: 10.1007/s10878-017-0183-4
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    References listed on IDEAS

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    1. Dorit S. Hochbaum & David B. Shmoys, 1985. "A Best Possible Heuristic for the k -Center Problem," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 180-184, May.
    2. Sourour Elloumi & Martine Labbé & Yves Pochet, 2004. "A New Formulation and Resolution Method for the p-Center Problem," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 84-94, February.
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