2026-07-26T02:16:03Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6390 2024-03-06T10:38:08Z ddc:004 open_access

Counting Linear Extensions: Parameterizations by Treewidth Eiben, Eduard Ganian, Robert Kangas, Kustaa Ordyniak, Sebastian Partially ordered sets Linear extensions Parameterized Complexity Structural parameters Treewidth 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Eduard Eiben and Robert Ganian and Kustaa Kangas and Sebastian Ordyniak 2016 Is Part Of LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2016.39 urn:nbn:de:0030-drops-63903 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.39 eng https://creativecommons.org/licenses/by/3.0/legalcode