Kernelizations for the hybridization number problem on multiple nonbinary trees

Given a finite set X, a collection Tof rooted phylogenetic trees on Xand an integerk, theHybridization Numberproblem asks if there exists a phylogenetic network onXthat displays all trees fromTand has reticulation number at mostk. We show two kernelization algorithms forHybridization Number, with kernel sizes 4k(5k)tand 20k2(+−1)respectively, withtthe 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 nf(k)t-time algorithm, with n =|X|and fsome computable function ofk.