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(n2) time per path and O(n2) 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.

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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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