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DOI: 10.4230/LIPIcs.SoCG.2018.18
URN: urn:nbn:de:0030-drops-87311
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8731/
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Burton, Benjamin A.

The HOMFLY-PT Polynomial is Fixed-Parameter Tractable

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LIPIcs-SoCG-2018-18.pdf (1 MB)


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.

BibTeX - Entry

@InProceedings{burton:LIPIcs:2018:8731,
  author =	{Benjamin A. Burton},
  title =	{{The HOMFLY-PT Polynomial is Fixed-Parameter Tractable}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8731},
  URN =		{urn:nbn:de:0030-drops-87311},
  doi =		{10.4230/LIPIcs.SoCG.2018.18},
  annote =	{Keywords: Knot theory, knot invariants, parameterised complexity}
}

Keywords: Knot theory, knot invariants, parameterised complexity
Seminar: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 24.05.2018


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