Inferring a Level-1 Phylogenetic Network from a Dense Set of Rooted Triplets

  • Jesper Jansson
  • Wing-Kin Sung
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3106)


Given a set \({\cal T}\) of rooted triplets with leaf set L, we consider the problem of determining whether there exists a phylogenetic network consistent with \({\mathcal{T}}\), and if so, constructing one. If no restrictions are placed on the hybrid nodes in the solution, the problem is trivially solved in polynomial time by a simple sorting network-based construction. For the more interesting (and biologically more motivated) case where the solution is required to be a level-1 phylogenetic network, we present an algorithm solving the problem in O(n6) time when \({\mathcal{T}}\) is dense (i.e., contains at least one rooted triplet for each cardinality three subset of L), where n = |L|. Note that the size of the input is Θ(n3) if \({\mathcal{T}}\) is dense. We also give an O(n5)-time algorithm for finding the set of all phylogenetic networks having a single hybrid node attached to exactly one leaf (and having no other hybrid nodes) that are consistent with a given dense set of rooted triplets.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jesper Jansson
    • 1
  • Wing-Kin Sung
    • 1
  1. 1.School of ComputingNational University of SingaporeSingapore

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