The Euclidean k-Supplier Problem in

Abstract

In this paper, we consider k-supplier problem in . Here, two sets of points $\mathcal{P}$ and $\mathcal{Q}$ are given. The objective is to choose a subset $Q_{opt} \subseteq \mathcal{Q}$ of size at most k such that congruent disks of minimum radius centered at the points in $Q_{opt}$ cover all the points of $\mathcal{P}$.

We propose a fixed-parameter tractable (FPT) algorithm for the k-supplier problem that produces a 2-factor approximation result. For $|P|=n$ and $|Q|=m$, the worst case running time of the algorithm is $O(6^k (n+m) \log (mn))$, 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 $(1+\sqrt{3})$-approximation algorithm, but the results produced by our algorithm significantly outperforms that of Nagarajan et al.’s algorithm.

Wireless & Geometry.