The Floodlight Problem

Given three angles summing to 2, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of speci ed angles not exceeding  can be placed at n xed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2. We give Onlogn algorithms for both these problems.

• Type: Conference
• Year: 1993
• Where: CCCG
• Authors: Prosenjit Bose, Leonidas J. Guibas, Anna Lubiw, Mark H. Overmars, Diane L. Souvaine, Jorge Urrutia
• Keywords: CCCG 1993, CCCG 2007, Entire Plane, Speci Ed Angles, Wedge Contains Ki