Eiben, E, Ganian, R, Kangas, K et al. (1 more author) (2019) Counting Linear Extensions: Parameterizations by Treewidth. Algorithmica, 81 (4). pp. 1657-1683. ISSN 0178-4617
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2018. This is an open access article under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | Partially ordered sets; Linear extensions; Parameterized complexity; Structural parameters; Treewidth |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Nov 2020 15:42 |
Last Modified: | 17 Nov 2020 15:42 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00453-018-0496-4 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:168075 |
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