Improved Algorithm for Enumerating Plane Triangulations

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.

Enumerating pseudo-triangulations in the plane

A pseudo-triangle is a simple polygon with exactly three convex vertices. A pseudo-triangulation of a finite point set S in the plane is a partition of the convex hull of S into interior disjoint pseudo-triangles whose vertices are points of S. A pointed pseudo-triangulation is one which has the least number of pseudo-triangles. We study the graph G whose vertices represent the pointed pseudo-t...

On the Enumeration of all Minimal Triangulations

We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where “proper” means that the tree decomposition cannot be improved by removing or splitting a bag.

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...