Abstract
We introduce a new measure for planar point sets S that captures a combinatorial distance that S is from being a convex set: The reflexivity p(S) of S is given by the smallest number of reflex vertices in a simple polygonalization of S. We prove combinatorial bounds on the reflexivity of point sets and study some closely related quantities, including the convex cover number k c (S) of a planar point set, which is the smallest number of convex chains that cover S, and the convex partition number k p (S), which is given by the smallest number of convex chains with pairwise-disjoint convex hulls that cover S.
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Arkin, E.M. et al. (2003). On the Reflexivity of Point Sets. In: Aronov, B., Basu, S., Pach, J., Sharir, M. (eds) Discrete and Computational Geometry. Algorithms and Combinatorics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55566-4_6
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DOI: https://doi.org/10.1007/978-3-642-55566-4_6
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