A faster tree-decomposition based algorithm for counting linear extensions
We consider the problem of counting the linear extensions of an n-element poset whose cover graph has treewidth at most t. We show that the problem can be solved in time Õ(nt+3), where Õ suppresses logarithmic factors. Our algorithm is based on fast multiplication of multivariate polynomials, and so...
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ftunivhelsihelda:oai:helda.helsinki.fi:10138/325877 2024-01-07T09:46:26+01:00 A faster tree-decomposition based algorithm for counting linear extensions Kangas, Kustaa Koivisto, M. Salonen, S. Paul, Christophe Pilipczuk, Michal Doctoral Programme in Computer Science Department of Computer Science University Management 2021-02-04T09:38:01Z 13 application/pdf http://hdl.handle.net/10138/325877 eng eng 10.4230/LIPIcs.IPEC.2018.5 13th International Symposium on Parameterized and Exact Computation (IPEC 2018) Leibniz International Proceedings in Informatics 978-3-95977-084-2 Kangas , K , Koivisto , M & Salonen , S 2019 , A faster tree-decomposition based algorithm for counting linear extensions . in C Paul & M Pilipczuk (eds) , 13th International Symposium on Parameterized and Exact Computation (IPEC 2018) . , 5 , Leibniz International Proceedings in Informatics , vol. 115 , Schloss Dagstuhl - Leibniz-Zentrum für Informatik , Dagstuhl , International Symposium on Parameterized and Exact Computation , Helsinki , Finland , 20/08/2018 . https://doi.org/10.4230/LIPIcs.IPEC.2018.5 conference Bibtex: Kangas2019 ORCID: /0000-0001-9662-3605/work/88205375 85090383078 cc6fde8f-5ec6-4a87-8276-a58940b85851 http://hdl.handle.net/10138/325877 cc_by openAccess info:eu-repo/semantics/openAccess Parameter estimation Counting linear extensions Cover graph Exclusion algorithms Fast multiplication Linear extensions Multivariate polynomial Running time Tree decomposition Trees (mathematics) 113 Computer and information sciences Conference contribution publishedVersion 2021 ftunivhelsihelda 2023-12-14T00:02:52Z We consider the problem of counting the linear extensions of an n-element poset whose cover graph has treewidth at most t. We show that the problem can be solved in time Õ(nt+3), where Õ suppresses logarithmic factors. Our algorithm is based on fast multiplication of multivariate polynomials, and so differs radically from a previous Õ(nt+4)-time inclusion–exclusion algorithm. We also investigate the algorithm from a practical point of view. We observe that the running time is not well characterized by the parameters n and t alone, fixing of which leaves large variance in running times due to uncontrolled features of the selected optimal-width tree decomposition. For selecting an efficient tree decomposition we adopt the method of empirical hardness models, and show that it typically enables picking a tree decomposition that is significantly more efficient than a random optimal-width tree decomposition. © Kustaa Kangas, Mikko Koivisto, and Sami Salonen; licensed under Creative Commons License CC-BY. Peer reviewed Conference Object sami HELDA – University of Helsinki Open Repository Kangas ENVELOPE(25.367,25.367,66.250,66.250) Koivisto ENVELOPE(26.486,26.486,67.052,67.052) |
institution |
Open Polar |
collection |
HELDA – University of Helsinki Open Repository |
op_collection_id |
ftunivhelsihelda |
language |
English |
topic |
Parameter estimation Counting linear extensions Cover graph Exclusion algorithms Fast multiplication Linear extensions Multivariate polynomial Running time Tree decomposition Trees (mathematics) 113 Computer and information sciences |
spellingShingle |
Parameter estimation Counting linear extensions Cover graph Exclusion algorithms Fast multiplication Linear extensions Multivariate polynomial Running time Tree decomposition Trees (mathematics) 113 Computer and information sciences Kangas, Kustaa Koivisto, M. Salonen, S. A faster tree-decomposition based algorithm for counting linear extensions |
topic_facet |
Parameter estimation Counting linear extensions Cover graph Exclusion algorithms Fast multiplication Linear extensions Multivariate polynomial Running time Tree decomposition Trees (mathematics) 113 Computer and information sciences |
description |
We consider the problem of counting the linear extensions of an n-element poset whose cover graph has treewidth at most t. We show that the problem can be solved in time Õ(nt+3), where Õ suppresses logarithmic factors. Our algorithm is based on fast multiplication of multivariate polynomials, and so differs radically from a previous Õ(nt+4)-time inclusion–exclusion algorithm. We also investigate the algorithm from a practical point of view. We observe that the running time is not well characterized by the parameters n and t alone, fixing of which leaves large variance in running times due to uncontrolled features of the selected optimal-width tree decomposition. For selecting an efficient tree decomposition we adopt the method of empirical hardness models, and show that it typically enables picking a tree decomposition that is significantly more efficient than a random optimal-width tree decomposition. © Kustaa Kangas, Mikko Koivisto, and Sami Salonen; licensed under Creative Commons License CC-BY. Peer reviewed |
author2 |
Paul, Christophe Pilipczuk, Michal Doctoral Programme in Computer Science Department of Computer Science University Management |
format |
Conference Object |
author |
Kangas, Kustaa Koivisto, M. Salonen, S. |
author_facet |
Kangas, Kustaa Koivisto, M. Salonen, S. |
author_sort |
Kangas, Kustaa |
title |
A faster tree-decomposition based algorithm for counting linear extensions |
title_short |
A faster tree-decomposition based algorithm for counting linear extensions |
title_full |
A faster tree-decomposition based algorithm for counting linear extensions |
title_fullStr |
A faster tree-decomposition based algorithm for counting linear extensions |
title_full_unstemmed |
A faster tree-decomposition based algorithm for counting linear extensions |
title_sort |
faster tree-decomposition based algorithm for counting linear extensions |
publishDate |
2021 |
url |
http://hdl.handle.net/10138/325877 |
long_lat |
ENVELOPE(25.367,25.367,66.250,66.250) ENVELOPE(26.486,26.486,67.052,67.052) |
geographic |
Kangas Koivisto |
geographic_facet |
Kangas Koivisto |
genre |
sami |
genre_facet |
sami |
op_relation |
10.4230/LIPIcs.IPEC.2018.5 13th International Symposium on Parameterized and Exact Computation (IPEC 2018) Leibniz International Proceedings in Informatics 978-3-95977-084-2 Kangas , K , Koivisto , M & Salonen , S 2019 , A faster tree-decomposition based algorithm for counting linear extensions . in C Paul & M Pilipczuk (eds) , 13th International Symposium on Parameterized and Exact Computation (IPEC 2018) . , 5 , Leibniz International Proceedings in Informatics , vol. 115 , Schloss Dagstuhl - Leibniz-Zentrum für Informatik , Dagstuhl , International Symposium on Parameterized and Exact Computation , Helsinki , Finland , 20/08/2018 . https://doi.org/10.4230/LIPIcs.IPEC.2018.5 conference Bibtex: Kangas2019 ORCID: /0000-0001-9662-3605/work/88205375 85090383078 cc6fde8f-5ec6-4a87-8276-a58940b85851 http://hdl.handle.net/10138/325877 |
op_rights |
cc_by openAccess info:eu-repo/semantics/openAccess |
_version_ |
1787428223950258176 |