Bulletin of Mathematical Biology

, Volume 75, Issue 10, pp 1879–1890 | Cite as

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

Original Article

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.

Keywords

Cherry Fixed-parameter tractability Phylogenetic network Phylogenetic tree Temporal network 

Notes

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.

Supplementary material

11538_2013_9874_MOESM1_ESM.pdf (244 kb)
Appendix A.1: Fixed-parameter tractability of 2-Minimum–Temporal Hybridization (PDF 244 kB)

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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  • Peter J. Humphries
    • 1
  • Simone Linz
    • 2
    • 3
  • Charles Semple
    • 3
  1. 1.Department of Mathematics and PhysicsNorth Carolina Central UniversityDurhamUSA
  2. 2.Center for BioinformaticsUniversity of TübingenTübingenGermany
  3. 3.Biomathematics Research Centre, Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand

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