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Discrete & Computational Geometry

, Volume 37, Issue 4, pp 545–563 | Cite as

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

  • Otfried Cheong
  • Alon Efrat
  • Sariel Har-Peled
Article

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.

Keywords

Grid Cell Voronoi Diagram Rigid Motion Uniform Sample Range Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Division of Computer Science, KAIST, Gwahangno 335, Yuseong-guDaejeon 305-701South Korea
  2. 2.Department of Computer Science, University of ArizonaTucson, AZ 85721USA
  3. 3.Department of Computer Science, University of Illinois, 201 N. Goodwin AvenueUrbana, IL 61801USA

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