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

## TL;DR

This paper introduces a fixed-parameter algorithm for constructing minimal reticulation tree-child networks from multiple binary trees, significantly improving efficiency and scalability over previous methods.

## Contribution

It presents the first fixed-parameter algorithm for this problem, utilizing cherry picking sequences and enabling handling of up to 100 input trees.

## Key findings

- Algorithm runs in $O((8k)^k ext{poly}(n, t))$ time.
- Parallel implementation can process up to 100 trees.
- Provides a major efficiency improvement over previous methods.

## Abstract

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 among all such networks. The algorithm uses the recently introduced framework of cherry picking sequences and runs in $O((8k)^k \mathrm{poly}(n, t))$ time, where $n$ is the number of leaves of every tree, $t$ is the number of trees, and $k$ is the reticulation number of the constructed network. Moreover, we provide an efficient parallel implementation of the algorithm and show that it can deal with up to $100$ input trees on a standard desktop computer, thereby providing a major improvement over previous phylogenetic network construction methods.