The Euclidean k-supplier problem in IR2

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Conference Article

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


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.

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