Finding a Guard that Sees Most and a Shop that Sells Most

Authors:
Otfried Cheong;Alon Efrat;Sariel Har-Peled
Affiliations:
Division of Computer Science, KAIST, Gwahangno 335, Yuseong-gu, Daejeon 305-701, South Korea;Department of Computer Science, University of Arizona, Tucson, AZ 85721, USA;Department of Computer Science, University of Illinois, 201 N. Goodwin Avenue, Urbana, IL 61801, USA
Venue:
Discrete & Computational Geometry
Year:
2007

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Abstract

We present a near-quadratic time algorithm that computes a point inside a simple polygon P in the plane having approximately the largest visibility polygon inside P, and a near-linear time algorithm for finding the point that will have approximately the largest Voronoi region when added to an n-point set in the plane. We apply the same technique to find the translation that approximately maximizes the area of intersection of two polygonal regions in near-quadratic time, and the rigid motion doing so in near-cubic time.