@inproceedings{76f5e33d9eb7480caacc4bdbee9f5aae,

title = "PTAS for geometric hitting set problems via local search",

abstract = "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 halfspaces 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.",

keywords = "Approximation algorithm, Epsilon nets, Hitting sets, Local search",

author = "Mustafa, {Nabil H.} and Saurabh Ray",

year = "2009",

doi = "10.1145/1542362.1542367",

language = "English (US)",

isbn = "9781605585017",

series = "Proceedings of the Annual Symposium on Computational Geometry",

pages = "17--22",

booktitle = "Proceedings of the 25th Annual Symposium on Computational Geometry, SCG'09",

note = "25th Annual Symposium on Computational Geometry, SCG'09 ; Conference date: 08-06-2009 Through 10-06-2009",

}