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Counting Cherry Reduction Sequences in Phylogenetic Tree-Child Networks is Counting Linear Extensions.

Tomás M Coronado1, Joan Carles Pons1, Gabriel Riera2

  • 1Department of Mathematics and Computer Science, Universitat de les Illes Balears, Ctra. de Valldemossa, km 7,5, 07122, Palma, Illes Balears, Spain.

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We present a novel method for analyzing tree-child networks by relating cherry deletion counts to poset linear extensions. This approach offers insights into network topology and computational complexity.

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Linear extensionsNetwork tree-widthOrchard networksPhylogenetic networksTree-child networks

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Area of Science:

  • Computational Biology
  • Phylogenetics
  • Network Theory

Background:

  • Orchard and tree-child networks, like phylogenetic trees, are reducible via cherry and reticulated cherry deletion.
  • The number of reduction sequences provides topological information for these networks.

Purpose of the Study:

  • To establish a computational framework for quantifying topological properties of tree-child networks.
  • To develop an efficient algorithm for counting network reduction sequences.

Main Methods:

  • Demonstrated the equivalence between counting cherry deletion sequences in tree-child networks and counting linear extensions of induced posets.
  • Developed a reduction-based algorithm for computing this count.

Main Results:

  • The problem of computing the number of reduction sequences is shown to be equivalent to finding linear extensions of the induced poset.
  • The proposed algorithm's complexity is bounded by the network's level.

Conclusions:

  • This work provides a novel algorithmic approach to analyze tree-child network topology.
  • The findings connect network reduction properties to poset theory, offering new avenues for research in phylogenetics and network analysis.