New FPT Algorithms for Finding the Temporal Hybridization Number for Sets of Phylogenetic Trees

New FPT Algorithms for Finding the Temporal Hybridization Number for Sets of Phylogenetic Trees

Borst, Sander (Centrum Wiskunde & Informatica (CWI))
van Iersel, L.J.J. (TU Delft Discrete Mathematics and Optimization)
Jones, M.E.L. (Centrum Wiskunde & Informatica (CWI))
Kelk, Steven (Universiteit Maastricht)

2022

We study the problem of finding a temporal hybridization network containing at most k 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 m binary trees with n leaves each with a running time of O(5 ^k· n· m). We also present the concept of temporal distance, which is a measure for how close a tree-child network is to being temporal. Then we introduce an algorithm for computing a tree-child network with temporal distance at most d and at most k reticulations in O((8 k) ^d5 ^k· k· n· m) time. Lastly, we introduce an O(6 ^kk! · k· n²) time algorithm for computing a temporal hybridization network for a set of two nonbinary trees. We also provide an implementation of all algorithms and an experimental analysis on their performance.

Hybridization number
Parameterized algorithms
Phylogenetic networks
Phylogenetic trees

http://resolver.tudelft.nl/uuid:27cf7e13-f21c-4332-821a-c0ba2646cd52

https://doi.org/10.1007/s00453-022-00946-8

0178-4617

Algorithmica, 84 (7), 2050-2087

Institutional Repository

journal article

© 2022 Sander Borst, L.J.J. van Iersel, M.E.L. Jones, Steven Kelk