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

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Hai Du & Yinfeng Xu

  2. School of Management, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Hai Du & Yinfeng Xu

  3. The State Key Lab for Manufacturing Systems Engineering, Xi’an, 710049, P.R. China

    Hai Du & Yinfeng Xu

Authors
  1. Hai Du
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  2. Yinfeng Xu
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Corresponding author

Correspondence to Hai Du.

Additional information

We would like to acknowledge the support from the NSF of China (No. 71071123, No. 60921003) and the PCSIRT of China (No. 1173).

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Du, H., Xu, Y. An approximation algorithm for k-center problem on a convex polygon. J Comb Optim 27, 504–518 (2014). https://doi.org/10.1007/s10878-012-9532-5

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  • DOI: https://doi.org/10.1007/s10878-012-9532-5

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