PARAMETERIZED COMPLEXITY OF UNTANGLING KNOTSast
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10491049" target="_blank" >RIV/00216208:11320/24:10491049 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=~hOnQLiwNj" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=~hOnQLiwNj</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/22M1501969" target="_blank" >10.1137/22M1501969</a>
Alternative languages
Result language
angličtina
Original language name
PARAMETERIZED COMPLEXITY OF UNTANGLING KNOTSast
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 in a shortest untangling sequence the II - moves, that is, the moves removing two adjacent crossings, 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
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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/GA22-19073S" target="_blank" >GA22-19073S: Combinatorial and computational complexity in topology and geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Computing
ISSN
0097-5397
e-ISSN
1095-7111
Volume of the periodical
53
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
49
Pages from-to
431-479
UT code for WoS article
001189705300002
EID of the result in the Scopus database
2-s2.0-85190577587