Counting Linear Extensions: Parameterizations by Treewidth
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00113714" target="_blank" >RIV/00216224:14330/19:00113714 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00453-018-0496-4" target="_blank" >https://doi.org/10.1007/s00453-018-0496-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00453-018-0496-4" target="_blank" >10.1007/s00453-018-0496-4</a>
Alternative languages
Result language
angličtina
Original language name
Counting Linear Extensions: Parameterizations by Treewidth
Original language description
We consider the #P-complete problem of counting the number of linear extensions of a poset (#LE); a fundamental problem in order theory with applications in a variety of distinct areas. In particular, we study the complexity of #LE parameterized by the well-known decompositional parameter treewidth for two natural graphical representations of the input poset, i.e., the cover and the incomparability graph. Our main result shows that #LE is fixed-parameter intractable parameterized by the treewidth of the cover graph. This resolves an open problem recently posed in the Dagstuhl seminar on Exact Algorithms. On the positive side we show that #LE becomes fixed-parameter tractable parameterized by the treewidth of the incomparability graph.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Algorithmica
ISSN
0178-4617
e-ISSN
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Volume of the periodical
81
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
1657-1683
UT code for WoS article
000465431800013
EID of the result in the Scopus database
2-s2.0-85053424850