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Deterministically Counting k-Paths and Trees Parameterized by Treewidth in Single-Exponential Time

Authors: Jonne Visser and Hans L. Bodlaender

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)


Abstract
In this paper, we give new and faster deterministic algorithms to count the number of k-paths and trees in host graphs of bounded treewidth. Our algorithms use time that is single-exponential in the treewidth, and employ the determinant method from [Hans L. Bodlaender et al., 2015]. Modifications of the algorithms count in single-exponential time the number of k-paths between specified end-points, the number of k-cycles, and the number of trees with k vertices that are a subgraph of the host graph.

Cite as

Jonne Visser and Hans L. Bodlaender. Deterministically Counting k-Paths and Trees Parameterized by Treewidth in Single-Exponential Time. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{visser_et_al:LIPIcs.IPEC.2025.20,
  author =	{Visser, Jonne and Bodlaender, Hans L.},
  title =	{{Deterministically Counting k-Paths and Trees Parameterized by Treewidth in Single-Exponential Time}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.20},
  URN =		{urn:nbn:de:0030-drops-251529},
  doi =		{10.4230/LIPIcs.IPEC.2025.20},
  annote =	{Keywords: Parameterized Complexity, Counting Subgraphs, #k-path, Dynamic Programming, Tree Decomposition, Determinant Method}
}
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