Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-triangles

  • O. Aichholzer
  • C. Huemer
  • S. Kappes
  • B. Speckmann
  • C. D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)

Abstract

We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties and give combinatorial bounds on their complexity. Our upper bounds depend on new Ramsey-type results concerning disjoint empty convex k-gons in point sets.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • O. Aichholzer
    • 1
  • C. Huemer
    • 2
  • S. Kappes
    • 3
  • B. Speckmann
    • 4
  • C. D. Tóth
    • 5
  1. 1.Institute for Software TechnologyGraz University of Technology 
  2. 2.Departament de Matemática Aplicada IIUniversitat Politécnica de Catalunya 
  3. 3.Department of MathematicsTU Berlin 
  4. 4.Department of Mathematics and Computer ScienceTU Eindhoven 
  5. 5.Department of MathematicsMassachusetts Institute of Technology 

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