On finding a guard that sees most and a shop that sells most
Otfried Cheong, Alon Efrat, Sariel Har-Peled · 2004
We present a near-quadratic time algorithm that computes a point inside a simple polygon P having approximately the largest visibility polygon inside P, and a nearlinear time algorithm for finding the point that will have approximately the largest Voronoi region when added to an n-point set. 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. 1