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

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


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.


Computational Geometry Convex Polygon Steiner Point Simple Polygon Convex Quadrilateral 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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