Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Maria, Clément https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-138527
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Parameterized Complexity of Quantum Knot Invariants

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Abstract

We give a general fixed parameter tractable algorithm to compute quantum invariants of links presented by planar diagrams, whose complexity is singly exponential in the carving-width (or the tree-width) of the diagram.
In particular, we get a O(N^{3/2 cw} poly(n)) ∈ N^O(√n) time algorithm to compute any Reshetikhin-Turaev invariant - derived from a simple Lie algebra 𝔤 - of a link presented by a planar diagram with n crossings and carving-width cw, and whose components are coloured with 𝔤-modules of dimension at most N. For example, this includes the N^{th}-coloured Jones polynomial.

BibTeX - Entry

@InProceedings{maria:LIPIcs.SoCG.2021.53,
  author =	{Maria, Cl\'{e}ment},
  title =	{{Parameterized Complexity of Quantum Knot Invariants}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{53:1--53:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13852},
  URN =		{urn:nbn:de:0030-drops-138527},
  doi =		{10.4230/LIPIcs.SoCG.2021.53},
  annote =	{Keywords: computational knot theory, parameterized complexity, quantum invariants}
}

Keywords: computational knot theory, parameterized complexity, quantum invariants
Seminar: 37th International Symposium on Computational Geometry (SoCG 2021)
Issue date: 2021
Date of publication: 02.06.2021


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