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: https://drops.dagstuhl.de/opus/volltexte/2019/10453/
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de Mesmay, Arnaud ; Rieck, Yo'av ; Sedgwick, Eric ; Tancer, Martin

The Unbearable Hardness of Unknotting

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LIPIcs-SoCG-2019-49.pdf (1.0 MB)


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}
}

Keywords: Knot, Link, NP-hard, Reidemeister move, Unknot recognition, Unlinking number, intermediate invariants
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019


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