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On the Number of Radial Orderings of Colored Planar Point Sets

  • José M. Díaz-Báñez
  • Ruy Fabila-Monroy
  • Pablo Pérez-Lantero
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

Abstract

Let n be an even natural number and let S be a set of n red and n blue points in general position in the plane. Let p ∉ S be a point such that S ∪ {p} is in general position. A radial ordering of S with respect to p is a circular ordering of the elements of S by angle around p. A colored radial ordering is a radial ordering of S in which only the colors of the points are considered. We show that: the number of distinct radial orderings of S is at most O(n4) and at least Ω(n2); the number of colored radial orderings of S is at most O(n4) and at least Ω(n); there exists sets of points with Θ(n4) colored radial orderings and sets of points with only O(n2) colored radial orderings.

Keywords

radial orderings colored point sets star polygonizations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • José M. Díaz-Báñez
    • 1
  • Ruy Fabila-Monroy
    • 2
  • Pablo Pérez-Lantero
    • 3
  1. 1.Departamento Matemática Aplicada IIUniversidad de SevillaSevilleSpain
  2. 2.Departamento de MatemáticasCentro de Investigación y Estudios Avanzados del Instituto Politécnico NacionalMexico CityMexico
  3. 3.Escuela de Ingeniería Civil en InformáticaUniversidad de ValparaísoValparaisoChile

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