An O(n log n) Algorithm for the All-Farthest-Segments Problem for a Planar Set of Points
نویسندگان
چکیده
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 logn) 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 logn) for this problem, where h is the number of vertices on the convex hull of P . © 2007 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Inf. Process. Lett.
دوره 105 شماره
صفحات -
تاریخ انتشار 2006