Skip lists: a probabilistic alternative to balanced trees
Communications of the ACM
A computer generated census of cusped hyperbolic 3-manifolds
Proceedings of the third conference on Computers and mathematics
A skip list cookbook
3-manifold knot genus is NP-complete
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithmic Topology and Classification of 3-Manifolds (Algorithms and Computation in Mathematics)
Algorithmic Topology and Classification of 3-Manifolds (Algorithms and Computation in Mathematics)
Enumeration of Non-Orientable 3-Manifolds Using Face-Pairing Graphs and Union-Find
Discrete & Computational Geometry
The complexity of the normal surface solution space
Proceedings of the twenty-sixth annual symposium on Computational geometry
The pachner graph and the simplification of 3-sphere triangulations
Proceedings of the twenty-seventh annual symposium on Computational geometry
Parameterized complexity of discrete morse theory
Proceedings of the twenty-ninth annual symposium on Computational geometry
| Hi-index | 0.00 |
Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms is that most combinatorial triangulations must be discarded because they do not represent topological 3-manifolds. In this paper we show how to preempt bad triangulations by detecting genus in partially-constructed vertex links, allowing us to prune the enumeration tree substantially. The key idea is to manipulate the boundary edges surrounding partial vertex links using expected logarithmic time operations. Practical testing shows the resulting enumeration algorithm to be significantly faster, with up to 249x speed-ups even for small problems where comparisons are feasible. We also discuss parallelisation, and describe new data sets that have been obtained using high-performance computing facilities.