On the all-farthest-segments problem for a planar set of points

Authors:
Asish Mukhopadhyay;Samidh Chatterjee;Benjamin Lafreniere
Affiliations:
School of Computer Science, University of Windsor, Windsor, Ontario, Canada;School of Computer Science, University of Windsor, Windsor, Ontario, Canada;School of Computer Science, University of Windsor, Windsor, Ontario, Canada
Venue:
Information Processing Letters
Year:
2006

Citing 2
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An O(nlogn) algorithm for the all-farthest-segments problem for a planar set of points

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Farthest segments and extremal triangles spanned by points in R3

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All-maximum and all-minimum problems under some measures

Journal of Discrete Algorithms

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Abstract

In this note, we outline a very simple algorithm for the following problem: Given a set S of n points p1, p2, p3,...,pn in the plane, we have O(n2) segments implicitly defined on pairs of these n points. For each point pi, find a segment from this set of implicitly defined segments that is farthest from pi. The time complexity of our algorithm is in O(nh+nlogn), where n is the number of input points, and h is the number of vertices on the convex hull of S.