# New FPT algorithms for finding the temporal hybridization number for sets of phylogenetic trees

@article{Borst2022NewFA,
title={New FPT algorithms for finding the temporal hybridization number for sets of phylogenetic trees},
author={Sander Borst},
journal={Algorithmica},
year={2022},
volume={84},
pages={2050-2087}
}
• Sander Borst
• Published 27 July 2020
• Computer Science
• Algorithmica
<jats:p>We study the problem of finding a temporal hybridization network containing at most <jats:italic>k</jats:italic> reticulations, for an input consisting of a set of phylogenetic trees. First, we introduce an FPT algorithm for the problem on an arbitrary set of <jats:italic>m</jats:italic> binary trees with <jats:italic>n</jats:italic> leaves each with a running time of <jats:inline-formula><jats:alternatives><jats:tex-math>$$O(5^k\cdot n\cdot m)$$</jats:tex-math><mml:math xmlns:mml="http…
2 Citations
A Practical Fixed-Parameter Algorithm for Constructing Tree-Child Networks from Multiple Binary Trees
• Computer Science
Algorithmica
• 2022
We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations
Orchard Networks are Trees with Additional Horizontal Arcs
• Biology
Bulletin of mathematical biology
• 2022
It is shown that orchard networks can be interpreted as trees with additional horizontal arcs, closely related to tree-based networks, where the difference is that in tree- based networks the additional arcs do not need to be horizontal.

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