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A linear time approximation scheme for computing geometric maximum k-star

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  • Jia Wang
  • Shiyan Hu

Abstract

Facility dispersion seeks to locate the facilities as far away from each other as possible, which has attracted a multitude of research attention recently due to the pressing need on dispersing facilities in various scenarios. In this paper, as a facility dispersion problem, the geometric maximum k-star problem is considered. Given a set P of n points in the Euclidean plane, a k-star is defined as selecting k points from P and linking k − 1 points to the center point. The maximum k-star problem asks to compute a k-star on P with the maximum total length over its k − 1 edges. A linear time approximation scheme is proposed for this problem. It approximates the maximum k-star within a factor of $${(1+\epsilon)}$$ in $${O(n+1/\epsilon^4 \log 1/\epsilon)}$$ time for any $${\epsilon >0 }$$ . To the best of the authors’ knowledge, this work presents the first linear time approximation scheme on the facility dispersion problems. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Jia Wang & Shiyan Hu, 2013. "A linear time approximation scheme for computing geometric maximum k-star," Journal of Global Optimization, Springer, vol. 55(4), pages 849-855, April.
  • Handle: RePEc:spr:jglopt:v:55:y:2013:i:4:p:849-855
    DOI: 10.1007/s10898-012-9867-6
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    References listed on IDEAS

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    1. Daniel J. Rosenkrantz & Giri K. Tayi & S.S. Ravi, 2000. "Facility Dispersion Problems Under Capacity and Cost Constraints," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 7-33, March.
    2. Erkut, Erhan, 1990. "The discrete p-dispersion problem," European Journal of Operational Research, Elsevier, vol. 46(1), pages 48-60, May.
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