Applications of Parametric Searching in Geometric Optimization

We present several applications in computational geometry of Megiddo's parametric searching technique. These applications include: (1) Finding the minimum Hausdorff distance under translation between two polygonal regions in the plane under the Euclidean metric; (2) Computing the biggest line segment that can be placed inside a simple polygon; (3) Computing the smallest width annulus that can contain a given set of points in the plane; (4) Solving the 1-segment center problem -- given a set of points in the plane, find a placement for a given line segment (under translation and rotation) which minimizes the largest distance from the segment to the given points; (5) Given a set of n points in 3-space, finding the largest radius r such that if we place a ball of radius r around each point, no segment connecting a pair of points is intersected by a third ball. Besides obtaining efficient solutions to all these problems (which, in every case, either improve considerably previous solu...

• Type: Conference
• Year: 1992
• Where: SODA
• Authors: Pankaj K. Agarwal, Micha Sharir, Sivan Toledo
• Keywords: Algorithms, National Science Foundation, Parametric Searching Technique, Science Foundation Grant, SODA 1992