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CORR
2002
Springer

On the Reflexivity of Point Sets

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On the Reflexivity of Point Sets
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 (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 c(S) of a planar point set, which is the smallest number of convex chains that cover S, and the convex partition number p(S), which is given by the smallest number of convex chains with pairwise-disjoint convex hulls that cover S.
Esther M. Arkin, Sándor P. Fekete, Ferran H
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2002
Where CORR
Authors Esther M. Arkin, Sándor P. Fekete, Ferran Hurtado, Joseph S. B. Mitchell, Marc Noy, Vera Sacristan, Saurabh Sethia
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