Maximum-Area Triangle in a Convex Polygon, Revisited [article]

Vahideh Keikha and Maarten Löffler and Ali Mohades and Jérôme Urhausen and Ivor van der Hoog
2017 arXiv   pre-print
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 n) time divide-and-conquer algorithm. Also we show by example that the algorithm presented in 1979 by Dobkin and Snyder for
more » ... 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.
arXiv:1705.11035v2 fatcat:2axjswqvujbhbhricckfxhtq6i