Kernelizations for the hybridization number problem on multiple nonbinary trees

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)(Delta(+) - 1) respectively, with t the number of input trees and Delta(+) 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 = vertical bar X vertical bar and f some computable function of k.