The Zigzag Path of a Pseudo-Triangulation

Authors

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

Document Type

Article

Publication Date

1-1-2003

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Abstract

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.

Volume

2748

First Page

377

Last Page

388

DOI

10.1007/978-3-540-45078-8_33

ISSN

03029743

Comments

Archived as published.

Recommended Citation

Aichholzer, Oswin; Rote, Günter; Speckmann, Bettina; and Streinu, Ileana, "The Zigzag Path of a Pseudo-Triangulation" (2003). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/270