A Faster Fixed-Parameter Approach to Drawing Binary Tanglegrams

  • Sebastian Böcker
  • Falk Hüffner
  • Anke Truss
  • Magnus Wahlström
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5917)

Abstract

Given two binary phylogenetic trees covering the same n species, it is useful to compare them by drawing them with leaves arranged side-by-side. To facilitate comparison, we would like to arrange the trees to minimize the number of crossings k induced by connecting pairs of identical species. This is the NP-hard Tanglegram Layout problem. By providing a fast transformation to the Balanced Subgraph problem, we show that the problem admits an O(2kn4) algorithm, improving upon a previous fixed-parameter approach with running time O(cknO(1)) where c ≈ 1000. We enhance a Balanced Subgraph implementation based on data reduction and iterative compression with improvements tailored towards these instances, and run experiments with real-world data to show the practical applicability of this approach. All practically relevant (k ≤ 1000) Tanglegram Layout instances can be solved exactly within seconds. Additionally, we provide a kernel-like bound by showing how to reduce the Balanced Subgraph instances for Tanglegram Layout on complete binary trees to a size of O(k logk).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sebastian Böcker
    • 1
  • Falk Hüffner
    • 2
  • Anke Truss
    • 1
  • Magnus Wahlström
    • 3
  1. 1.Lehrstuhl für BioinformatikFriedrich-Schiller-Universität JenaJenaGermany
  2. 2.Algorithms in Computational Genomics group, School of Computer ScienceTel Aviv UniversityTel AvivIsrael
  3. 3.Max-Planck-Institut für Informatik, Department 1: Algorithms and ComplexitySaarbrückenGermany

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