Parallel Enumeration of Triangulations

TL;DR

This paper introduces a parallel algorithm called down-flip reverse search for enumerating all regular triangulations of finite point sets, significantly improving scalability and enabling the handling of larger datasets, with applications in tropical geometry.

Contribution

The paper presents a novel parallel algorithm for enumerating triangulations, enhancing scalability and efficiency over previous methods.

Findings

Enables computation of larger triangulations than before.

Supports massive parallelization for improved scalability.

Applicable to tropical geometry problems.

Abstract

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 parallelization, i.e., it scales well even for many cores. Our implementation allows to compute the triangulations of much larger point sets than before.