The complexity of detecting taut angle structures on triangulations
Abstract
There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manifold triangulation, whose existence has implications for both the geometry and combinatorics of the triangulation. We prove that detecting taut angle structures is NP-complete, but also fixed-parameter tractable in the treewidth of the face pairing graph of the triangulation. These results have deeper implications: the core techniques can serve as a launching point for approaching decision problems such as unknot recognition and prime decomposition of 3-manifolds.
Keywords
Cite
@article{arxiv.1207.0904,
title = {The complexity of detecting taut angle structures on triangulations},
author = {Benjamin A. Burton and Jonathan Spreer},
journal= {arXiv preprint arXiv:1207.0904},
year = {2019}
}
Comments
22 pages, 10 figures, 3 tables; v2: minor updates. To appear in SODA 2013: Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms