Maximum-Area Quadrilateral in a Convex Polygon, Revisited

TL;DR

This paper revisits the problem of finding the maximum-area quadrilateral inscribed in a convex polygon, demonstrating that a well-known 1979 algorithm does not always produce the optimal solution for k=4.

Contribution

It provides a counterexample showing the failure of the Dobkin and Snyder algorithm for k=4, addressing an open question about its correctness.

Findings

The Dobkin and Snyder algorithm fails for k=4 in some convex polygons.

The failure extends the known limitations of the algorithm beyond k=3.

The paper clarifies the boundaries of the algorithm's applicability.

Abstract

In this note 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. This question, posed by Keikha et al. where they showed that the Dobkin Snyder algorithm fails for k=3.