Algorithmica

, Volume 68, Issue 4, pp 886–915

Constructing Minimal Phylogenetic Networks from Softwired Clusters is Fixed Parameter Tractable

Article

DOI: 10.1007/s00453-012-9708-5

Cite this article as:
Kelk, S. & Scornavacca, C. Algorithmica (2014) 68: 886. doi:10.1007/s00453-012-9708-5

Abstract

Here we show that, given a set of clusters \({\mathcal{C}}\) on a set of taxa \({\mathcal{X}}\), where \(|{\mathcal{X}}|=n\), it is possible to determine in time f(k)⋅poly(n) whether there exists a level-≤k network (i.e. a network where each biconnected component has reticulation number at most k) that represents all the clusters in \({\mathcal{C}}\) in the softwired sense, and if so to construct such a network. This extends a result from Kelk et al. (in IEEE/ACM Trans. Comput. Biol. Bioinform. 9:517–534, 2012) which showed that the problem is polynomial-time solvable for fixed k. By defining “k-reticulation generators” analogous to “level-k generators”, we then extend this fixed parameter tractability result to the problem where k refers not to the level but to the reticulation number of the whole network.

Keywords

PhylogeneticsFixed parameter tractabilityDirected acyclic graphs

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Knowledge Engineering (DKE)Maastricht UniversityMaastrichtThe Netherlands
  2. 2.ISEM, UMR 5554, CNRSUniv. Montpellier 2MontpellierFrance