Linear time Minimum Area All-flush Triangles Circumscribing a Convex Polygon

12/14/2017

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by   Kai Jin, et al.

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We study the problem of computing the minimum area triangle that circumscribes a given n-sided convex polygon touching edge-to-edge. In other words, we compute the minimum area triangle that is the intersection of 3 half-planes out of n half-planes defined by a given convex polygon. Building on the Rotate-and-Kill technique Arxiv:1707.04071, we propose an algorithm that solves the problem in O(n) time, improving the best-known O(n n) time algorithms given in [A. Aggarwal et. al. DCG94; B. Schieber. SODA95. Our algorithm computes all the locally minimal area circumscribing triangles touching edge-to-edge.