Multitriangulations, pseudotriangulations and primitive sorting networks

We study the set of all pseudoline arrangements with contact points which cover a given support. We define a notion of flip which transforms a pseudoline arrangement with contact points into another one with the same support, and we 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 relationship with sorting networks. Our algorithm requires a polynomial running time per arrangement and its working space is 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 with contact points covering a certain support. This interpretation explains their common properties and leads to a natural definition of multipseudotriangulations, which generalizes them. We study the elementary properties of these multipseudotriangulatio...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Vincent Pilaud, Michel Pocchiola
• Keywords: Contact Points, CORR 2010, Education, Enumeration Algorithm, Pseudoline Arrangements