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Polynomial time approximation schemes for minimum disk cover problems

Author

Listed:
  • Chen Liao

    (Michigan Technological University)

  • Shiyan Hu

    (Michigan Technological University)

Abstract

The following planar minimum disk cover problem is considered in this paper: given a set $\mathcal{D}$ of n disks and a set ℘ of m points in the Euclidean plane, where each disk covers a subset of points in ℘, to compute a subset of disks with minimum cardinality covering ℘. This problem is known to be NP-hard and an algorithm which approximates the optimal disk cover within a factor of (1+ε) in $\mathcal{O}(mn^{\mathcal{O}(\frac{1}{\epsilon^{2}}\log^{2}\frac{1}{\epsilon})})$ time is proposed in this paper. This work presents the first polynomial time approximation scheme for the minimum disk cover problem where the best known algorithm can approximate the optimal solution with a large constant factor. Further, several variants of the minimum disk cover problem such as the incongruent disk cover problem and the weighted disk cover problem are considered and approximation schemes are designed.

Suggested Citation

  • Chen Liao & Shiyan Hu, 2010. "Polynomial time approximation schemes for minimum disk cover problems," Journal of Combinatorial Optimization, Springer, vol. 20(4), pages 399-412, November.
    • Handle: RePEc:spr:jcomop:v:20:y:2010:i:4:d:10.1007_s10878-009-9216-y
    DOI: 10.1007/s10878-009-9216-y
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    References listed on IDEAS

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    1. Weiping Shang & Frances Yao & Pengjun Wan & Xiaodong Hu, 2008. "On minimum m-connected k-dominating set problem in unit disc graphs," Journal of Combinatorial Optimization, Springer, vol. 16(2), pages 99-106, August.
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    Cited by:

    1. Briskorn, Dirk & Dienstknecht, Michael, 2020. "Covering polygons with discs: The problem of crane selection and location on construction sites," Omega, Elsevier, vol. 97(C).

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