The Zigzag Path of a Pseudo-Triangulation

Oswin Aichholzer, Graz University of Technology, Institute of Software Technology
Günter Rote, Freie Universität Berlin
Bettina Speckmann, ETH Zürich
Ileana Streinu, Smith College

Archived as published.


We define the zigzag path of a pseudo-triangulation, a concept generalizing the path of a triangulation of a point set. The pseudotriangulation 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 pseudotriangulation 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 pseudotriangulations of a point set. © Springer-Verlag Berlin Heidelberg 2003.