The HOMFLY-PT polynomial is fixed-parameter tractable
Geometric Topology
2017-12-18 v1 Computational Geometry
Abstract
Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter tractable in the treewidth of the link diagram, but the parameterised complexity of the more powerful HOMFLY-PT polynomial remained an open problem. Here we show that computing HOMFLY-PT is fixed-parameter tractable in the treewidth, and we give the first sub-exponential time algorithm to compute it for arbitrary links.
Keywords
Cite
@article{arxiv.1712.05776,
title = {The HOMFLY-PT polynomial is fixed-parameter tractable},
author = {Benjamin A. Burton},
journal= {arXiv preprint arXiv:1712.05776},
year = {2017}
}
Comments
15 pages, 4 figures