The Euclidean k-supplier problem in IR2

Document Type

Conference Article

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Abstract

In this paper, we consider k-supplier problem in IR2. Here, two sets of points P and Q are given. The objective is to choose a subset Qopt ⊆ Q of size at most k such that congruent disks of minimum radius centered at the points in Qopt cover all the points of P. We propose a fixed-parameter tractable (FPT) algorithm for the ksupplier problem that produces a 2-factor approximation result. For |P| = n and |Q| = m, the worst case running time of the algorithm is O(6k(n + m) log(mn)), which is an exponential function of the parameter k. We also propose a heuristic algorithm based on Voronoi diagram for the k-supplier problem, and experimentally compare the result produced by this algorithm with the best known approximation algorithm available in the literature [Nagarajan, V., Schieber, B., Shachnai, H.: The Euclidean k-supplier problem, In Proc. of 16th Int. Conf. on Integ. Prog. and Comb. Optim., 290–301 (2013)]. The experimental results show that our heuristic algorithm is slower than Nagarajan et al.’s (1+ √3)-approximation algorithm, but the results produced by our algorithm significantly outperforms that of Nagarajan et al.’s algorithm.

First Page

129

Last Page

140

DOI

10.1007/978-3-319-53058-1_9

Publication Date

1-1-2017

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