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

Authors Jonne Visser , Hans L. Bodlaender

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Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Parameterized Complexity
  • Counting Subgraphs
  • #k-path
  • Dynamic Programming
  • Tree Decomposition
  • Determinant Method

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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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.IPEC.2025.20

Author Details

Jonne Visser
  • Utrecht University, The Netherlands
Hans L. Bodlaender
  • Utrecht University, The Netherlands

References

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