In the k-supplier problem, we are given a set of clients C and set of facilities F located in a metric (C∪F, d), along with a bound k. The goal is to open a subset of k facilities so as to minimize the maximum distance of a client to an open facility, i.e., minS⊆F: |S|=kmax v∈C d(v,S), where d(v,S) = minu∈S d(v,u) is the minimum distance of client v to any facility in S. We present a 1 + √3 < 2.74 approximation algorithm for the k-supplier problem in Euclidean metrics. This improves the previously known 3-approximation algorithm [9] which also holds for general metrics (where it is known to be tight). It is NP-hard to approximate Euclidean k-supplier to better than a factor of √7 ≈ 2.65, even in dimension two [5]. Our algorithm is based on a relation to the edge cover problem. We also present a nearly linear O(n·log2 n) time algorithm for Euclidean k-supplier in constant dimensions that achieves an approximation ratio of 2.965, where n = |C∪F|. © 2013 Springer-Verlag.
CITATION STYLE
Nagarajan, V., Schieber, B., & Shachnai, H. (2013). The Euclidean k-supplier problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7801 LNCS, pp. 290–301). https://doi.org/10.1007/978-3-642-36694-9_25
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