The mixed center location problem

Yi Xu (), Jigen Peng and Yinfeng Xu
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Yi Xu: Xi’an Jiaotong University
Jigen Peng: Xi’an Jiaotong University
Yinfeng Xu: Xi’an Jiaotong University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 4, No 3, 1128-1144

Abstract: Abstract This paper studies a new version of the location problem called the mixed center location problem. Let P be a set of n points in the plane. We first consider the mixed 2-center problem, where one of the centers must be in P, and we solve it in $$O(n^2\log n)$$ O ( n 2 log n ) time. Second, we consider the mixed k-center problem, where m of the centers are in P, and we solve it in $$O(n^{m+O(\sqrt{k-m})})$$ O ( n m + O ( k - m ) ) time. Motivated by two practical constraints, we propose two variations of the problem. Third, we present a 2-approximation algorithm and three heuristics solving the mixed k-center problem ( $$k>2$$ k > 2 ).

Keywords: k-Center problem; Facility location problem; Voronoi diagram; Computational geometry (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0183-4

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