On the Reflexivity of Point Sets

  title={On the Reflexivity of Point Sets},
  author={Esther M. Arkin and S{\'a}ndor P. Fekete and Ferran Hurtado and Joseph S. B. Mitchell and Marc Noy and Vera Sacrist{\'a}n Adinolfi and Saurabh Sethia},
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 ρ(S) of S is given by the smallest number of reflex vertices in a simple polygonalization of S. We prove various combinatorial bounds and provide efficient algorithms to compute reflexivity, both exactly (in special cases) and approximately (in general). Our study considers also some closely related quantities, such as the convex cover number κc(S) of a… CONTINUE READING