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CORR
2010
Springer

Multitriangulations, pseudotriangulations and primitive sorting networks

8 years 8 months ago
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...
Vincent Pilaud, Michel Pocchiola
Added 24 Jan 2011
Updated 24 Jan 2011
Type Journal
Year 2010
Where CORR
Authors Vincent Pilaud, Michel Pocchiola
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