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

We propose a novel subdivision of the plane that consists of both convex polygons and pseudotriangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudoconvex 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.

• Type: Journal
• Year: 2007
• Where: GC
• Authors: Oswin Aichholzer, Clemens Huemer, S. Kappes, Bettina Speckmann, Csaba D. Tóth
• Keywords: Applied Computing, Convex Polygons, GC 2007, Planar Point Sets, Point Sets