Abstract
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.