, Volume 68, Issue 4, pp 886-915

Constructing Minimal Phylogenetic Networks from Softwired Clusters is Fixed Parameter Tractable

Purchase on Springer.com

$39.95 / €34.95 / £29.95*

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.