Counting and Enumerating Pointed Pseudotriangulations with the Greedy Flip Algorithm

Authors:
Herve´ Bro¨nnimann;Lutz Kettner;Michel Pocchiola;Jack Snoeyink
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Computing
Year:
2006

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Abstract

We present an algorithm to enumerate the pointed pseudotriangulations of a given point set, based on the greedy flip algorithm of Pocchiola and Vegter [Discrete Comput. Geom. 16 (1996), pp. 419-453]. Our two independent implementations agree and allow us to experimentally verify or disprove conjectures on the numbers of pointed pseudotriangulations and triangulations of a given point set. (For example, we establish that the number of triangulations is bounded by the number of pointed pseudotriangulations for all sets of up to 10 points.)