An incremental version of the k-center problem on boundary of a convex polygon

Hai Du (), Yinfeng Xu () and Binhai Zhu ()
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Hai Du: Xi’an Jiaotong University
Yinfeng Xu: Xi’an Jiaotong University
Binhai Zhu: Montana State University

Journal of Combinatorial Optimization, 2015, vol. 30, issue 4, No 25, 1219-1227

Abstract: Abstract This paper studies an incremental version of the k-center problem with centers constrained to lie on boundary of a convex polygon. In the incremental k-center problem we considered, we are given a set of n demand points inside a convex polygon, facilities are constrained to lie on its boundary. Our algorithm produces an incremental sequence of facility sets $$B_{1}\subseteq B_{2}\subseteq \cdots \subseteq B_{n}$$ B 1 ⊆ B 2 ⊆ ⋯ ⊆ B n , where each $$B_{k}$$ B k contains k facilities. Such an algorithm is called $$\alpha $$ α -competitive, if for any k, the maximum of the ratio between the value of solution $$B_{k}$$ B k and the value of an optimal k-center solution is no more than $$\alpha $$ α . We present a polynomial time incremental algorithm with a competitive ratio $$\frac{3\sqrt{3}}{2}$$ 3 3 2 and we also prove a lower bound of 2.

Keywords: k-center; Facility location; Incremental algorithm; Competitive ratio (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-015-9933-3

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