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.
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Wang, J., Hu, S. A linear time approximation scheme for computing geometric maximum k-star. J Glob Optim 55, 849–855 (2013). https://doi.org/10.1007/s10898-012-9867-6
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DOI: https://doi.org/10.1007/s10898-012-9867-6