Faster Computation of the Robinson-Foulds Distance between Phylogenetic Networks

  • Tetsuo Asano
  • Jesper Jansson
  • Kunihiko Sadakane
  • Ryuhei Uehara
  • Gabriel Valiente
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6129)

Abstract

The Robinson-Foulds distance, which is the most widely used metric for comparing phylogenetic trees, has recently been generalized to phylogenetic networks. Given two networks N1,N2 with n leaves, m nodes, and e edges, the Robinson-Foulds distance measures the number of clusters of descendant leaves that are not shared by N1 and N2. The fastest known algorithm for computing the Robinson-Foulds distance between those networks runs in O(m(m + e)) time. In this paper, we improve the time complexity to O(n(m + e)/logn) for general networks and O(nm/logn) for general networks with bounded degree, and to optimal O(m + e) time for planar phylogenetic networks and bounded-level phylogenetic networks. We also introduce the natural concept of the minimum spread of a phylogenetic network and show how the running time of our new algorithm depends on this parameter. As an example, we prove that the minimum spread of a level-k phylogenetic network is at most k + 1, which implies that for two level-k phylogenetic networks, our algorithm runs in O((k + 1)(m + e)) time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tetsuo Asano
    • 1
  • Jesper Jansson
    • 2
  • Kunihiko Sadakane
    • 3
  • Ryuhei Uehara
    • 1
  • Gabriel Valiente
    • 4
  1. 1.School of Information ScienceJapan Advanced Institute of Science and TechnologyIshikawaJapan
  2. 2.Ochanomizu UniversityTokyoJapan
  3. 3.National Institute of InformaticsTokyoJapan
  4. 4.Algorithms, Bioinformatics, Complexity and Formal Methods Research GroupTechnical University of CataloniaBarcelonaSpain

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