Finding a Largest-Area Triangle in a Terrain in Near-Linear Time

04/23/2021

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by   Sergio Cabello, et al.

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A terrain is an x-monotone polygon whose lower boundary is a single line segment. We present an algorithm to find in a terrain a triangle of largest area in O(n log n) time, where n is the number of vertices defining the terrain. The best previous algorithm for this problem has a running time of O(n^2).