Embedding Phylogenetic Trees in Networks of Low Treewidth

Authors Leo van Iersel, Mark Jones , Mathias Weller

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Author Details

Leo van Iersel
  • Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands
Mark Jones
  • Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands
Mathias Weller
  • CNRS, LIGM (UMR 8049), Champs-s/-Marne, France


We are extremely grateful to the anonymous reviewers for their many insightful and helpful comments.

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Leo van Iersel, Mark Jones, and Mathias Weller. Embedding Phylogenetic Trees in Networks of Low Treewidth. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 69:1-69:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called Tree Containment, arises when validating networks constructed by phylogenetic inference methods. We present the first algorithm for (rooted) Tree Containment using the treewidth t of the input network N as parameter, showing that the problem can be solved in 2^O(t²)⋅|N| time and space.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • fixed-parameter tractability
  • treewidth
  • phylogenetic tree
  • phylogenetic network
  • display graph
  • tree containment
  • embedding


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