@article{Eppstein1992FindingMA,
title={Finding Minimum Area k-gons},
author={David Eppstein and Mark H. Overmars and G{\"u}nter Rote and Gerhard J. Woeginger},
journal={Discrete & Computational Geometry},
year={1992},
volume={7},
pages={45-58}
}

Given a set P of n points in the plane and a number k, we want to find a polygon C with vertices in P of minimum area that satisfies one of the following properties: (1) C is a convex k-gon, (2) C is an empty convex k-gon, or (3) C is the convex hull of exactly k points of P . We give algorithms for solving each of these three problems in time O(kn3). The space complexity is O(n) for k = 4 and O(kn2) for k ≥ 5. The algorithms are based on a dynamic programming approach. We generalize this… CONTINUE READING