Computing a Smallest Multi-labeled Phylogenetic Tree from Rooted Triplets

  • Sylvain Guillemot
  • Jesper Jansson
  • Wing-Kin Sung
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)


We investigate the computational complexity of a new combinatorial problem of inferring a smallest possible multi-labeled phylogenetic tree (MUL tree) which is consistent with each of the rooted triplets in a given set. We prove that even the restricted case of determining if there exists a MUL tree consistent with the input and having just one leaf duplication is NP-hard. Furthermore, we show that the general minimization problem is NP-hard to approximate within a ratio of n 1 − ε for any constant 0 < ε ≤ 1, where n denotes the number of distinct leaf labels in the input set, although a simple polynomial-time approximation algorithm achieves the approximation ratio n. We also provide an exact algorithm for the problem running in O *(7 n ) time and O *(3 n ) space.


Directed Graph Internal Node Chromatic Number Phylogenetic Network Lower Common Ancestor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sylvain Guillemot
    • 1
  • Jesper Jansson
    • 2
  • Wing-Kin Sung
    • 3
    • 4
  1. 1.Institut Gaspard MongeUniversité Paris-EstMarne-la-ValléeFrance
  2. 2.Ochanomizu UniversityTokyoJapan
  3. 3.School of ComputingNational University of SingaporeSingapore
  4. 4.Genome Institute of SingaporeGenomeSingapore

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