Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On the discrete unit disk cover problem
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Wireless coverage with disparate ranges
MobiHoc '11 Proceedings of the Twelfth ACM International Symposium on Mobile Ad Hoc Networking and Computing
Geometric packing under non-uniform constraints
Proceedings of the twenty-eighth annual symposium on Computational geometry
Approximating low-dimensional coverage problems
Proceedings of the twenty-eighth annual symposium on Computational geometry
Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve
Computational Geometry: Theory and Applications
Exact algorithms and APX-hardness results for geometric packing and covering problems
Computational Geometry: Theory and Applications
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We consider the problem of computing minimum geometric hitting sets in which, given a set of geometric objects and a set of points, the goal is to compute the smallest subset of points that hit all geometric objects. The problem is known to be strongly NP-hard even for simple geometric objects like unit disks in the plane. Therefore, unless P = NP, it is not possible to get Fully Polynomial Time Approximation Algorithms (FPTAS) for such problems. We give the first PTAS for this problem when the geometric objects are half-spaces in ℝ3 and when they are an r-admissible set regions in the plane (this includes pseudo-disks as they are 2-admissible). Quite surprisingly, our algorithm is a very simple local-search algorithm which iterates over local improvements only.