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

  • Authors:

  • Jia Wang;Shiyan Hu

  • Affiliations:

  • Department of Electrical and Computer Engineering, Michigan Technological University, Houghton, USA 49931;Department of Electrical and Computer Engineering, Michigan Technological University, Houghton, USA 49931

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2013

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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 驴 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 驴 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.