Kernelizations for the hybridization number problem on multiple nonbinary trees

Leo van Iersel (1) , Steven Kelk (2) , Celine Scornavacca (3)

1 Department of Mathematics and Statistics [Christchurch]
2 Department of data science and Knowledge Engineering [Maastricht]
3 UMR ISEM - Institut des Sciences de l'Evolution de Montpellier

Given a finite set X, a collection T of rooted phylogenetic trees on X and an integer k, the Hybridization Number problem asks if there exists a phylogenetic network on X that displays all trees from T and has reticulation number at most k. We show two kernelization algorithms for Hybridization Number, with kernel sizes 4k(5k) t and 20k 2 (∆ + − 1) respectively, with t the number of input trees and ∆ + their maximum outdegree. Experiments on simulated data demonstrate the practical relevance of our kernelization algorithms. In addition, we present an n f (k) t-time algorithm, with n = |X| and f some computable function of k.

Mots clés: Fixed-parameter tractability; kernelization; phylogenetic tree; phylogenetic network; hybridization number

Domaines: Informatique [cs]; Bio-informatique [q-bio.QM]

Leo van Iersel, Steven Kelk, Celine Scornavacca. Kernelizations for the hybridization number problem on multiple nonbinary trees. Journal of Computer and System Sciences, 2016, 82 (6), pp.1075-1089. ⟨10.1016/j.jcss.2016.03.006⟩. ⟨hal-02154926⟩