Parameterized Complexity of Untangling Knots
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10454436" target="_blank" >RIV/00216208:11320/22:10454436 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.ICALP.2022.88" target="_blank" >https://doi.org/10.4230/LIPIcs.ICALP.2022.88</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2022.88" target="_blank" >10.4230/LIPIcs.ICALP.2022.88</a>
Alternative languages
Result language
angličtina
Original language name
Parameterized Complexity of Untangling Knots
Original language description
Deciding whether a diagram of a knot can be untangled with a given number of moves (as a part of the input) is known to be NP-complete. In this paper we determine the parameterized complexity of this problem with respect to a natural parameter called defect. Roughly speaking, it measures the efficiency of the moves used in the shortest untangling sequence of Reidemeister moves. We show that the II- moves in a shortest untangling sequence can be essentially performed greedily. Using that, we show that this problem belongs to W[P] when parameterized by the defect. We also show that this problem is W[P]-hard by a reduction from Minimum axiom set.
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GJ19-04113Y" target="_blank" >GJ19-04113Y: Advanced tools in combinatorics, topology and related areas</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Leibniz International Proceedings in Informatics, LIPIcs
ISBN
978-3-95977-235-8
ISSN
1868-8969
e-ISSN
—
Number of pages
17
Pages from-to
1-17
Publisher name
Schloss Dagstuhl
Place of publication
Dagstuhl
Event location
Francie
Event date
Jul 4, 2022
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—