Maximum-Area Triangle in a Convex Polygon, Revisited

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 [1] 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 logn) time divide-and-conquer algorithm. Also we show by example that the algorithm presented in 1979 by Dobkin and Snyder [1] 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.