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.

• 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
• Keywords: Convex Chains, CORR 2002, Education, Planar Point, Smallest Number