Abstract
In this note, we outline a very simple algorithm for the following problem: Given a set S of n points p 1 , p 2 , p 3 , … , p n in the plane, we have O ( n 2 ) segments implicitly defined on pairs of these n points. For each point p i , find a segment from this set of implicitly defined segments that is farthest from p i . The time complexity of our algorithm is in O ( n h + n log n ) , where n is the number of input points, and h is the number of vertices on the convex hull of S.
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