Discrete & Computational Geometry

, Volume 48, Issue 1, pp 142–191 | Cite as

Multitriangulations, Pseudotriangulations and Primitive Sorting Networks

Article

Abstract

We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration algorithm for arrangements with a given support, based on the properties of certain greedy pseudoline arrangements and on their connection with sorting networks. Both the running time per arrangement and the working space of our algorithm are polynomial.

As the motivation for this work, we provide in this paper a new interpretation of both pseudotriangulations and multitriangulations in terms of pseudoline arrangements on specific supports. This interpretation explains their common properties and leads to a natural definition of multipseudotriangulations, which generalizes both. We study elementary properties of multipseudotriangulations and compare them to iterations of pseudotriangulations.

Keywords

Pseudoline arrangement Pseudotriangulation Multitriangulation Flip Sorting network Enumeration algorithm 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.CNRS & LIX (UMR 7161)École PolytechniquePalaiseauFrance
  2. 2.Institut de Mathématiques de Jussieu (UMR 7586)Université Pierre et Marie CurieParisFrance

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