License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.49
URN: urn:nbn:de:0030-drops-104530
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10453/
de Mesmay, Arnaud ;
Rieck, Yo'av ;
Sedgwick, Eric ;
Tancer, Martin
The Unbearable Hardness of Unknotting
Abstract
We prove that deciding if a diagram of the unknot can be untangled using at most k Reidemeister moves (where k is part of the input) is NP-hard. We also prove that several natural questions regarding links in the 3-sphere are NP-hard, including detecting whether a link contains a trivial sublink with n components, computing the unlinking number of a link, and computing a variety of link invariants related to four-dimensional topology (such as the 4-ball Euler characteristic, the slicing number, and the 4-dimensional clasp number).
BibTeX - Entry
@InProceedings{demesmay_et_al:LIPIcs:2019:10453,
author = {Arnaud de Mesmay and Yo'av Rieck and Eric Sedgwick and Martin Tancer},
title = {{The Unbearable Hardness of Unknotting}},
booktitle = {35th International Symposium on Computational Geometry (SoCG 2019)},
pages = {49:1--49:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-104-7},
ISSN = {1868-8969},
year = {2019},
volume = {129},
editor = {Gill Barequet and Yusu Wang},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10453},
URN = {urn:nbn:de:0030-drops-104530},
doi = {10.4230/LIPIcs.SoCG.2019.49},
annote = {Keywords: Knot, Link, NP-hard, Reidemeister move, Unknot recognition, Unlinking number, intermediate invariants}
}
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Keywords: |
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Knot, Link, NP-hard, Reidemeister move, Unknot recognition, Unlinking number, intermediate invariants |
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Collection: |
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35th International Symposium on Computational Geometry (SoCG 2019) |
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Issue Date: |
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2019 |
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Date of publication: |
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11.06.2019 |
