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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)

Abstract

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.

Keywords

Directed Graph Internal Node Chromatic Number Phylogenetic Network Lower Common Ancestor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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