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

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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.

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Notes

  1. We use [m] to denote the set of integers \(\{1, \ldots , m\}\) and \([m]_0\) to denote the set of integers \(\{0, \ldots , m\}\).

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Acknowledgements

We would like to thank the anonymous reviewers for valuable comments that helped us improve this manuscript.

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, Van Mourik Broekmanweg 6, 2628 XE, Delft, The Netherlands

    Leo van Iersel, Remie Janssen, Mark Jones & Yukihiro Murakami

  2. Faculty of Computer Science, Dalhousie University, 6050 University Ave, Halifax, NS, B3H 1W5, Canada

    Norbert Zeh

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  1. Leo van Iersel
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  2. Remie Janssen
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  3. Mark Jones
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  4. Yukihiro Murakami
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  5. Norbert Zeh
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Correspondence to Norbert Zeh.

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Leo van Iersel, Remie Janssen, Mark Jones and Yukihiro Murakami were supported by the Netherlands Organization for Scientific Research (NWO), including Vidi grant 639.072.602, and van Iersel also by the 4TU Applied Mathematics Institute. Norbert Zeh was supported by the Natural Sciences and Engineering Research Council of Canada.

A Construction of a Tree-Child Network from a Tree-Child Cherry Picking Sequence

A Construction of a Tree-Child Network from a Tree-Child Cherry Picking Sequence

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van Iersel, L., Janssen, R., Jones, M. et al. A Practical Fixed-Parameter Algorithm for Constructing Tree-Child Networks from Multiple Binary Trees. Algorithmica 84, 917–960 (2022). https://doi.org/10.1007/s00453-021-00914-8

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  • DOI: https://doi.org/10.1007/s00453-021-00914-8

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