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

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Abstract

Recently, we have shown that calculating the minimum–temporal-hybridization number for a set \({\mathcal{P}}\) of rooted binary phylogenetic trees is NP-hard and have characterized this minimum number when \({\mathcal{P}}\) consists of exactly two trees. In this paper, we give the first characterization of the problem for \({\mathcal{P}}\) being arbitrarily large. The characterization is in terms of cherries and the existence of a particular type of sequence. Furthermore, in an online appendix to the paper, we show that this new characterization can be used to show that computing the minimum–temporal hybridization number for two trees is fixed-parameter tractable.

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Acknowledgements

We thank the referees for their helpful comments. S.L. was supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme. C.S. was supported by the New Zealand Marsden Fund and the Allan Wilson Centre for Molecular Ecology and Evolution.

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Author notes

  1. Simone Linz

    Present address: Biomathematics Research Centre, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

Authors and Affiliations

  1. Department of Mathematics and Physics, North Carolina Central University, Durham, NC, USA

    Peter J. Humphries

  2. Center for Bioinformatics, University of Tübingen, Tübingen, Germany

    Simone Linz

  3. Biomathematics Research Centre, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

    Charles Semple

Authors
  1. Peter J. Humphries
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  2. Simone Linz
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  3. Charles Semple
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Correspondence to Simone Linz.

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Humphries, P.J., Linz, S. & Semple, C. Cherry Picking: A Characterization of the Temporal Hybridization Number for a Set of Phylogenies. Bull Math Biol 75, 1879–1890 (2013). https://doi.org/10.1007/s11538-013-9874-x

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  • DOI: https://doi.org/10.1007/s11538-013-9874-x

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