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Determining the Consistency of Resolved Triplets and Fan Triplets

  • Jesper JanssonEmail author
  • Andrzej Lingas
  • Ramesh Rajaby
  • Wing-Kin Sung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10229)

Abstract

The \(\mathcal {R}^{+-} \mathcal {F}^{+-}\) Consistency problem takes as input two sets \(R^{+}\) and \(R^{-}\) of resolved triplets and two sets \(F^{+}\) and \(F^{-}\) of fan triplets, and asks for a distinctly leaf-labeled tree that contains all elements in \(R^{+} \cup F^{+}\) and no elements in \(R^{-} \cup F^{-}\) as embedded subtrees, if such a tree exists. This paper presents a detailed characterization of how the computational complexity of the problem changes under various restrictions. Our main result is an efficient algorithm for dense inputs satisfying \(R^{-} = \emptyset \) whose running time is linear in the size of the input and therefore optimal.

Keywords

Phylogenetic tree Rooted triplets consistency Algorithm Computational complexity 

Notes

Acknowledgments

The authors would like to thank Sylvain Guillemot and Avraham Melkman for some discussions related to the topic of this paper. J.J. was partially funded by The Hakubi Project at Kyoto University and KAKENHI grant number 26330014.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jesper Jansson
    • 1
    • 2
    Email author
  • Andrzej Lingas
    • 3
  • Ramesh Rajaby
    • 4
    • 5
  • Wing-Kin Sung
    • 4
    • 6
  1. 1.Laboratory of Mathematical Bioinformatics, ICRKyoto UniversityGokasho, Uji, KyotoJapan
  2. 2.Department of ComputingThe Hong Kong Polytechnic UniversityKowloonHong Kong, China
  3. 3.Department of Computer ScienceLund UniversityLundSweden
  4. 4.School of ComputingNational University of SingaporeSingaporeSingapore
  5. 5.NUS Graduate School for Integrative Sciences and EngineeringNational University of SingaporeSingaporeSingapore
  6. 6.Genome Institute of SingaporeSingaporeSingapore

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