Parallel Enumeration of Triangulations

Parallel Enumeration of Triangulations

We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing full triangulations only; this case is particularly relevant for tropical geometry. Most importantly, down-flip reverse search allows for massive parallelizati...

Ranked Enumeration of Minimal Triangulations

Tree decompositions facilitate computations on complex graphs by grouping vertices into bags interconnected in an acyclic structure; hence their importance in a plethora of problems such as query evaluation over databases and inference over probabilistic graphical models. Different applications take varying benefits from different tree decompositions, and hence, measure them by diverse (sometim...

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.

An efficient algorithm for enumeration of triangulations

Efficient enumeration of 3-manifold triangulations

Triangulations describe how different low-dimensional topological spaces can be constructed from simple building blocks. Forming an exhaustive list of all small triangulations is difficult, typically involving a slow computer-based search. We present techniques for improving the efficiency of such searches, thereby allowing more extensive lists to be constructed.