Level-k Phylogenetic Networks Are Constructable from a Dense Triplet Set in Polynomial Time

  • Thu-Hien To
  • Michel Habib
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5577)


For a given dense triplet set \(\mathcal{T}\), there exist two natural questions [7]: Does there exist any phylogenetic network consistent with \(\mathcal{T}\)? In case such networks exist, can we find an effective algorithm to construct one? For cases of networks of levels k = 0, 1 or 2, these questions were answered in [1,6,7,8,10] with effective polynomial algorithms. For higher levels k, partial answers were recently obtained in [11] with an \(O(|\mathcal{T}|^{k+1})\) time algorithm for simple networks. In this paper, we give a complete answer to the general case, solving a problem proposed in [7]. The main idea of our proof is to use a special property of SN-sets in a level-k network. As a consequence, for any fixed k, we can also find a level-k network with the minimum number of reticulations, if one exists, in polynomial time.


Polynomial Time Time Algorithm Simple Network Phylogenetic Network Lateral Gene Transfer Event 
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

  • Thu-Hien To
    • 1
  • Michel Habib
    • 1
  1. 1.LIAFA, CNRS and University Paris DiderotParis 7France

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