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arXiv · 1705.11035

Maximum-Area Triangle in a Convex Polygon, Revisited

Vahideh Keikha·Maarten Löffler·Ali Mohades·Jérôme Urhausen·Ivor van der Hoog
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Abstract

We revisit the following problem: Given a convex polygon $P$, find the largest-area inscribed triangle. We show by example that the linear-time algorithm presented in 1979 by Dobkin and Snyder for solving this problem fails. We then proceed to show that with a small adaptation, their approach does lead to a quadratic-time algorithm. We also present a more involved $O(n\log n)$ time divide-and-conquer algorithm. Also we show by example that the algorithm presented in 1979 by Dobkin and Snyder for finding the largest-area $k$-gon that is inscribed in a convex polygon fails to find the optimal solution for $k=4$. Finally, we discuss the implications of our discoveries on the literature.

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Vahideh Keikha, Maarten Löffler, Ali Mohades, Jérôme Urhausen, Ivor van der Hoog. 2017-05-31. Maximum-Area Triangle in a Convex Polygon, Revisited. https://doi.org/10.1016/j.ipl.2020.105943

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