Maximum-Area Triangle in a Convex Polygon, Revisited
Computational Geometry
2020-05-11 v2
Abstract
We revisit the following problem: Given a convex polygon , 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 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 -gon that is inscribed in a convex polygon fails to find the optimal solution for . Finally, we discuss the implications of our discoveries on the literature.
Cite
@article{arxiv.1705.11035,
title = {Maximum-Area Triangle in a Convex Polygon, Revisited},
author = {Vahideh Keikha and Maarten Löffler and Ali Mohades and Jérôme Urhausen and Ivor van der Hoog},
journal= {arXiv preprint arXiv:1705.11035},
year = {2020}
}