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Finding Maximum Common Contractions Between Phylogenetic Networks

Authors Bertrand Marchand , Nadia Tahiri , Olivier Tremblay-Savard , Manuel Lafond

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Bertrand Marchand
  • Department of Computer Science, University of Sherbrooke, Canada
Nadia Tahiri
  • Department of Computer Science, University of Sherbrooke, Canada
Olivier Tremblay-Savard
  • Department of Computer Science, University of Manitoba, Winnipeg, Canada
Manuel Lafond
  • Department of Computer Science, University of Sherbrooke, Canada

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Bertrand Marchand, Nadia Tahiri, Olivier Tremblay-Savard, and Manuel Lafond. Finding Maximum Common Contractions Between Phylogenetic Networks. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 16:1-16:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.WABI.2024.16

Abstract

In this paper, we lay the groundwork on the comparison of phylogenetic networks based on edge contractions and expansions as edit operations, as originally proposed by Robinson and Foulds to compare trees. We prove that these operations connect the space of all phylogenetic networks on the same set of leaves, even if we forbid contractions that create cycles. This allows to define an operational distance on this space, as the minimum number of contractions and expansions required to transform one network into another. We highlight the difference between this distance and the computation of the maximum common contraction between two networks. Given its ability to outline a common structure between them, which can provide valuable biological insights, we study the algorithmic aspects of the latter. We first prove that computing a maximum common contraction between two networks is NP-hard, even when the maximum degree, the size of the common contraction, or the number of leaves is bounded. We also provide lower bounds to the problem based on the Exponential-Time Hypothesis. Nonetheless, we do provide a polynomial-time algorithm for weakly galled trees, a generalization of galled trees.

Subject Classification

ACM Subject Classification
  • Applied computing → Bioinformatics
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Phylogenetic networks
  • contractions
  • algorithms
  • weakly galled trees

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