Finding Minimum Area k-Gons (1992) [18 citations — 4 self]
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author = {David Eppstein and Mark Overmars and Günter Rote and Gerhard Woeginger},
title = {Finding Minimum Area k-Gons},
journal = {Discrete Comput. Geom},
year = {1992},
volume = {7},
pages = {45--58}
}
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Abstract:
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(kn 3 ). The space complexity is O(n) for k = 4 and O(kn 2 ) for k # 5. The algorithms are based on a dynamic programming approach. We generalize this approach to polygons with minimum perimeter, polygons with maximum perimeter or area, polygons containing the maximum or minimum number of points, polygons with minimum weight (for some weights added to vertices), etc., in similar time bounds. # This paper includes work done while David Eppstein was at Columbia University, Department of Computer Science, and while Gunter Rote and Gerhard Woeginger were at the Freie Universitat Berlin, Fachbereich Mathematik, Institut fur Informatik....
