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arXiv · 2007.13615

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

Sander Borst·Leo van Iersel·Mark Jones·Steven Kelk
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Abstract

We study the problem of finding a temporal hybridization network for a set of phylogenetic trees that minimizes the number of reticulations. First, we introduce an FPT algorithm for this problem on an arbitrary set of $m$ binary trees with $n$ leaves each with a running time of $O(5^k\cdot n\cdot m)$, where $k$ is the minimum temporal hybridization number. 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 $O((8k)^d5^ k\cdot n\cdot m)$ time. Lastly, we introduce a $O(6^kk!\cdot k\cdot n^2)$ time algorithm for computing a minimum 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.

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Sander Borst, Leo van Iersel, Mark Jones, Steven Kelk. 2020-07-27. New FPT algorithms for finding the temporal hybridization number for sets of phylogenetic trees. https://doi.org/10.1007/s00453-022-00946-8

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