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


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.


Grid Cell Voronoi Diagram Rigid Motion Uniform Sample Range Space 
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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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