License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2021.53
URN: urn:nbn:de:0030-drops-138527
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13852/
Maria, Clément
Parameterized Complexity of Quantum Knot Invariants
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 ? - of a link presented by a planar diagram with n crossings and carving-width cw, and whose components are coloured with ?-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}
}
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Keywords: |
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computational knot theory, parameterized complexity, quantum invariants |
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Collection: |
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37th International Symposium on Computational Geometry (SoCG 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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02.06.2021 |
