# 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} }

<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 ScienceAlgorithmica
- 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

- BiologyBulletin 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.

## References

SHOWING 1-10 OF 27 REFERENCES

A Practical Fixed-Parameter Algorithm for Constructing Tree-Child Networks from Multiple Binary Trees

- Computer ScienceAlgorithmica
- 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…

On the complexity of computing the temporal hybridization number for two phylogenies

- BiologyDiscret. Appl. Math.
- 2013

Computing the minimum number of hybridization events for a consistent evolutionary history

- Computer ScienceDiscret. Appl. Math.
- 2007

Cherry Picking: A Characterization of the Temporal Hybridization Number for a Set of Phylogenies

- MathematicsBulletin of mathematical biology
- 2013

The first characterization of the problem for the minimum–temporal-hybridization number for a set of rooted binary phylogenetic trees being arbitrarily large is given, in terms of cherries and the existence of a particular type of sequence.

Kernelizations for the hybridization number problem on multiple nonbinary trees

- Computer ScienceJ. Comput. Syst. Sci.
- 2016

Comparison of Tree-Child Phylogenetic Networks

- BiologyIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2009

An injective representation of these networks as multisets of vectors of natural numbers, their path multiplicity vectors are provided, and this representation is used to define a distance on this class that extends the well-known Robinson-Foulds distance for phylogenetic trees and to give an alignment method for pairs of networks in this class.

A Cluster Reduction for Computing the Subtree Distance Between Phylogenies

- Computer Science
- 2011

A divide-and-conquer approach to calculating the rSPR distance is established that breaks the problem instance into a number of smaller and more tractable subproblems and shows that this distance is fixed-parameter tractable.

A Simple Fixed Parameter Tractable Algorithm for Computing the Hybridization Number of Two (Not Necessarily Binary) Trees

- BiologyIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2013

Here, we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted, not necessarily binary phylogenetic trees on taxon set X in time (6rr!) · poly(n),…

Hybridization in Nonbinary Trees

- BiologyIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2009

It is shown that the NP-hard problem of calculating the minimum number of reticulation events for two (arbitrary) rooted phylogenetic trees parameterized by this minimum number is fixed-parameter tractable.

How reticulated are species?

- BiologyBioEssays : news and reviews in molecular, cellular and developmental biology
- 2016

Many groups of closely related species have reticulate phylogenies, showing that some sexual compatibility may exist among them and can affect all parts of the tree of life, not just the recent species at the tips.