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An approximation algorithm for k-center problem on a convex polygon

Author

Listed:
  • Hai Du

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

  • Yinfeng Xu

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

Abstract

This paper studies the constrained version of the k-center location problem. Given a convex polygonal region, every point in the region originates a service demand. Our objective is to place k facilities lying on the region’s boundary, such that every point in that region receives service from its closest facility and the maximum service distance is minimized. This problem is equivalent to covering the polygon by k circles with centers on its boundary which have the smallest possible radius. We present an 1.8841-approximation polynomial time algorithm for this problem.

Suggested Citation

  • Hai Du & Yinfeng Xu, 2014. "An approximation algorithm for k-center problem on a convex polygon," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 504-518, April.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:3:d:10.1007_s10878-012-9532-5
    DOI: 10.1007/s10878-012-9532-5
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    Cited by:

    1. Yi Xu & Jigen Peng & Wencheng Wang & Binhai Zhu, 2018. "The connected disk covering problem," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 538-554, February.
    2. Xiaozhou He & Zhihui Liu & Bing Su & Yinfeng Xu & Feifeng Zheng & Binhai Zhu, 2019. "Efficient algorithms for computing one or two discrete centers hitting a set of line segments," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1408-1423, May.

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