Enumerating pseudo-triangulations in the plane

Enumerating pseudo-triangulations in the plane

Counting and enumerating pseudo-triangulations with the greedy flip algorithm∗

This paper studies pseudo-triangulations for a given point set in the plane. Pseudo-triangulations have many properties of triangulations, and have more freedom since polygons with more than three vertices are allowed as long as they have exactly inner angles less than π. In particular, there is a natural flip operation on every internal edge. We establish fundamental properties of pseudo-trian...

Counting and Enumerating Pointed Pseudo-triangulations with the Greedy Flip Algorithm

This paper studies (pointed, or minimal) pseudotriangulations for a given point set in the plane. Pseudotriangulations have many properties of triangulations, and have more freedom since polygons with more than three vertices are allowed as long as exactly three have angles less than π. In particular, there is a natural flip operation on every internal edge. We establish fundamental properties ...

An e cient algorithm for enumeration of triangulations

We consider the problem of enumerating triangulations of n points in the plane in general position. We introduce a tree of triangulations and present an algorithm for enumerating triangulations in O(log log n) time per triangulation. It improves the previous bound by almost linear factor.

Improved Algorithm for Enumerating Plane Triangulations

In this paper we give an algorithm to generate all biconnected plane triangulations having exactly n vertices including exactly r vertices on the outer face. The algorithm uses O(n) space in total and generates such triangulations without duplications in O(rn) time per triangulation, while the previous best algorithm generates such triangulations in O(rn) time per triangulation.