A Practical Approximation Algorithm for Solving Massive Instances of Hybridization Number

  • Leo van Iersel
  • Steven Kelk
  • Nela Lekić
  • Celine Scornavacca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7534)


Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. In practice, exact solvers struggle to solve instances with reticulation number larger than 40. For such instances, one has to resort to heuristics and approximation algorithms. Here we present the algorithm CycleKiller which is the first approximation algorithm that can produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations. Theoretically, the algorithm is an exponential-time 2-approximation (or 4-approximation in its fastest mode). However, using simulations we demonstrate that in practice the algorithm runs quickly for large and difficult instances, producing solutions within one percent of optimality. An implementation of this algorithm, which extends the theoretical work of [14], has been made publicly available.


Phylogenetic Network Massive Instance Agreement Forest Hybridization Number Binary Phylogenetic Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Leo van Iersel
    • 1
  • Steven Kelk
    • 2
  • Nela Lekić
    • 2
  • Celine Scornavacca
    • 3
  1. 1.Centrum Wiskunde & Informatica (CWI)AmsterdamThe Netherlands
  2. 2.Department of Knowledge Engineering (DKE)Maastricht UniversityMaastrichtThe Netherlands
  3. 3.Institut des Sciences de l’Evolution (ISEM, UMR 5554 CNRS)Université Montpellier IIMontpellier Cedex 5France

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