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The Maximum Agreement of Two Nested Phylogenetic Networks

  • Jesper Jansson
  • Wing-Kin Sung
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3341)

Abstract

Given a set \({\mathcal N}\) of phylogenetic networks, the maximum agreement phylogenetic subnetwork problem (MASN) asks for a subnetwork contained in every \(N_{i} \in {\mathcal N}\) with as many leaves as possible. MASN can be used to identify shared branching structure among phylogenetic networks or to measure their similarity. In this paper, we prove that the general case of MASN is NP-hard already for two phylogenetic networks, but that the problem can be solved efficiently if the two given phylogenetic networks exhibit a nested structure. We first show that the total number of nodes |V(N)| in any nested phylogenetic network N with n leaves and nesting depth d is O(n (d +1)). We then describe an algorithm for testing if a given phylogenetic network is nested, and if so, determining its nesting depth in O(|V(N)| · (d + 1)) time. Next, we present a polynomial-time algorithm for MASN for two nested phylogenetic networks N 1, N 2. Its running time is O(|V(N 1)| · |V(N 2)| · (d 1 + 1) · (d 2 + 1)), where d 1 and d 2 denote the nesting depths of N 1 and N 2, respectively. In contrast, the previously fastest algorithm for this problem runs in O(|V(N 1)| · |V(N 2)| · 4 f ) time, where f ≥ max{d 1,d 2}.

Keywords

Directed Edge Outgoing Edge Phylogenetic Network Incoming Edge Input Tree 
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 2004

Authors and Affiliations

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

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