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Journal of Combinatorial Optimization

, Volume 13, Issue 3, pp 223–242 | Cite as

Fast algorithms for computing the tripartition-based distance between phylogenetic networks

  • Nguyen Bao Nguyen
  • C. Thach Nguyen
  • Wing-Kin SungEmail author
Article

Abstract

Consider two phylogenetic networks \({\cal N}\) and \({\cal N}\)’ of size n. The tripartition-based distance finds the proportion of tripartitions which are not shared by \({\cal N}\) and \({\cal N}\)’. This distance is proposed by Moret et al. (2004) and is a generalization of Robinson-Foulds distance, which is orginally used to compare two phylogenetic trees. This paper gives an \(O(\min \{k n \log n, n \log n + hn\})\)-time algorithm to compute this distance, where h is the number of hybrid nodes in \({\cal N}\) and \({\cal N}\)’ while k is the maximum number of hybrid nodes among all biconnected components in \({\cal N}\) and \({\cal N}\)’. Note that $k \ll h \ll n$ in a phylogenetic network. In addition, we propose algorithms for comparing galled-trees, which are an important, biological meaningful special case of phylogenetic network. We give an $O(n)$-time algorithm for comparing two galled-trees. We also give an \(O(n + kh)\)-time algorithm for comparing a galled-tree with another general network, where h and k are the number of hybrid nodes in the latter network and its biggest biconnected component respectively.

Keywords

Phylogenetic network Tripartition-based distance Algorithm 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Nguyen Bao Nguyen
    • 1
  • C. Thach Nguyen
    • 1
  • Wing-Kin Sung
    • 1
    Email author
  1. 1.National University of SingaporeSingaporeSingapore

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