DROPS

Document

DOI: 10.4230/LIPIcs.IPEC.2018.5

A Faster Tree-Decomposition Based Algorithm for Counting Linear Extensions

Authors: Kustaa Kangas, Mikko Koivisto, and Sami Salonen

Published in: LIPIcs, Volume 115, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

Abstract

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 O~(n^{t+3}), where O~ suppresses logarithmic factors. Our algorithm is based on fast multiplication of multivariate polynomials, and so differs radically from a previous O~(n^{t+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.

Cite as

Kustaa Kangas, Mikko Koivisto, and Sami Salonen. A Faster Tree-Decomposition Based Algorithm for Counting Linear Extensions. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{kangas_et_al:LIPIcs.IPEC.2018.5,
  author =	{Kangas, Kustaa and Koivisto, Mikko and Salonen, Sami},
  title =	{{A Faster Tree-Decomposition Based Algorithm for Counting Linear Extensions}},
  booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-084-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{115},
  editor =	{Paul, Christophe and Pilipczuk, Michal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2018.5},
  URN =		{urn:nbn:de:0030-drops-102062},
  doi =		{10.4230/LIPIcs.IPEC.2018.5},
  annote =	{Keywords: Algorithm selection, empirical hardness, linear extension, multiplication of polynomials, tree decomposition}
}

Document

DOI: 10.4230/LIPIcs.ESA.2016.39

Counting Linear Extensions: Parameterizations by Treewidth

Authors: Eduard Eiben, Robert Ganian, Kustaa Kangas, and Sebastian Ordyniak

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

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.

Cite as

Eduard Eiben, Robert Ganian, Kustaa Kangas, and Sebastian Ordyniak. Counting Linear Extensions: Parameterizations by Treewidth. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 39:1-39:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{eiben_et_al:LIPIcs.ESA.2016.39,
  author =	{Eiben, Eduard and Ganian, Robert and Kangas, Kustaa and Ordyniak, Sebastian},
  title =	{{Counting Linear Extensions: Parameterizations by Treewidth}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{39:1--39:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.39},
  URN =		{urn:nbn:de:0030-drops-63903},
  doi =		{10.4230/LIPIcs.ESA.2016.39},
  annote =	{Keywords: Partially ordered sets, Linear extensions, Parameterized Complexity, Structural parameters, Treewidth}
}

Search Results

Documents authored by Kangas, Kustaa

A Faster Tree-Decomposition Based Algorithm for Counting Linear Extensions

Abstract

Cite as

Counting Linear Extensions: Parameterizations by Treewidth

Abstract

Cite as

Thanks for your feedback!

Could not send message