Optimizing the double description method for normal surface enumeration
Abstract
Many key algorithms in 3-manifold topology involve the enumeration of normal surfaces, which is based upon the double description method for finding the vertices of a convex polytope. Typically we are only interested in a small subset of these vertices, thus opening the way for substantial optimization. Here we give an account of the vertex enumeration problem as it applies to normal surfaces, and present new optimizations that yield strong improvements in both running time and memory consumption. The resulting algorithms are tested using the freely available software package Regina.
Cite
@article{arxiv.0808.4050,
title = {Optimizing the double description method for normal surface enumeration},
author = {Benjamin A. Burton},
journal= {arXiv preprint arXiv:0808.4050},
year = {2011}
}
Comments
27 pages, 12 figures; v2: Removed the 3^n bound from Section 3.3, fixed the projective equation in Lemma 4.4, clarified "most triangulations" in the introduction to section 5; v3: replace -ise with -ize for Mathematics of Computation (note that this changes the title of the paper)