Finding extremal polygons

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Abstract

Given n points in the plane, we present algorithms for rinding maximum perimeter or area convex k-gons with vertices k of the given n points. Our algorithms work in linear space and time O(kn lgn + n lg2n). For the special case k = 3 we give O(n lg n) algorithms for these problems. Several related issues arc discussed.

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Boyce, J. E., Dobkin, D. P., Drysdale, R. L., & Guibas, L. J. (1982). Finding extremal polygons. In Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 282–289). Association for Computing Machinery. https://doi.org/10.1145/800070.802202

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