The Zigzag Path of a Pseudo-Triangulation

  • Oswin Aichholzer
  • Günter Rote
  • Bettina Speckmann
  • Ileana Streinu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)

Abstract

We define the zigzag path of a pseudo-triangulation, a concept generalizing the path of a triangulation of a point set. The pseudo-triangulation zigzag path allows us to use divide-and-conquer type of approaches for suitable (i.e., decomposable) problems on pseudo-triangulations. For this we provide an algorithm that enumerates all pseudo-triangulation zigzag paths (of all pseudo-triangulations of a given point set with respect to a given line) in O(n 2) time per path and O(n 2) space, where n is the number of points. We illustrate applications of our scheme which include a novel algorithm to count the number of pseudo-triangulations of a point set.

Keywords

Simple Polygon Partial Path Convex Corner Zigzag Path Reverse Search 
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 2003

Authors and Affiliations

  • Oswin Aichholzer
    • 1
  • Günter Rote
    • 2
  • Bettina Speckmann
    • 3
  • Ileana Streinu
    • 4
  1. 1.Institute for Software TechnologyGraz University of Technology 
  2. 2.Institute of Computer ScienceFU Berlin 
  3. 3.Institute for Theoretical Computer ScienceETH Zürich 
  4. 4.Department of Computer ScienceSmith College 

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