Optimal cover of points by disks in a simple polygon

Authors:
Haim Kaplan;Matthew J. Katz;Gila Morgenstern;Micha Sharir
Affiliations:
School of Computer Science, Tel Aviv University, Tel Aviv, Israel;Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel;Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel;School of Computer Science, Tel Aviv University, Tel Aviv, Israel, and Courant Institute of Mathematical Sciences, New York University, New York, NY
Venue:
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Year:
2010

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Abstract

Let P be a simple polygon, and let Q be a set of points in P. We present an almost-linear time algorithm for computing a minimum cover of Q by disks that are contained in P. We generalize the algorithm above, so that it can compute a minimum cover of Q by homothets of any fixed compact convex set O of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [20]. We also consider the disk-cover problem when Q is contained in a (not too wide) annulus, and present a nearly linear algorithm for this case too.