An O(n log n) Algorithm for the All-Farthest-Segments Problem for a Planar Set of Points

In this paper, we propose an algorithm for computing the farthest-segment Voronoi diagram for the edges of a convex polygon and apply this to obtain an O(n log n) algorithm for the following proximity problem: Given a set P of n(> 2) points in the plane, we have O(n2 ) implicitly defined segments on pairs of points. For each point p P, find a segment from this set of implicitly defined segments that is farthest from p. We improve the previously known time bound of O(nh+n log n) for this problem, where h is the number of vertices on the convex hull of P.

• Type: Conference
• Year: 2006
• Where: CCCG
• Authors: Asish Mukhopadhyay, Robert L. Scot Drysdale
• Keywords: CCCG 2006, CCCG 2007, Convex Polygon, Farthest-segment Voronoi Diagram, Implicitly Defined