Practical and efficient algorithms for the geometric hitting set problem

Abstract : The geometric hitting set problem is one of the basic geometric combinatorial optimization problems: given a set P of points and a set D of geometric objects in the plane, the goal is to compute a small-sized subset of P that hits all objects in D. Recently Agarwal and Pan [7] presented a near-linear time algorithm for the case where D consists of disks in the plane. The algorithm uses sophisticated geometric tools and data structures with large resulting constants. In this paper, we design a hitting-set algorithm for this case without the use of these data-structures, and present experimental evidence that our new algorithm has near-linear running time in practice, and computes hitting sets within 1.3-factor of the optimal hitting set. We further present dnet, a public source-code module that incorporates this improvement, enabling fast and efficient computation of small-sized hitting sets in practice.
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Norbert Bus, Nabil Mustafa, Saurabh Ray. Practical and efficient algorithms for the geometric hitting set problem. Discrete Applied Mathematics, Elsevier, 2018, 240, pp.25 - 32. ⟨10.1016/j.dam.2017.12.018⟩. ⟨hal-01797815⟩

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