An O(nlogn) algorithm for the all-farthest-segments problem for a planar set of points

Authors:
R. L. Scot Drysdale;Asish Mukhopadhyay
Affiliations:
Department of Computer Science, Dartmouth College, Hannover, NH, USA;School of Computer Science, University of Windsor, Canada
Venue:
Information Processing Letters
Year:
2008

Citing 5
Cited 2

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All-maximum and all-minimum problems under some measures

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Abstract

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(nlogn) algorithm for the following proximity problem: Given a set P of n (2) points in the plane, we have O(n^2) 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+nlogn) for this problem, where h is the number of vertices on the convex hull of P.