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 20k2(Δ+−1) respectively, with t the number of input trees and Δ+ 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 f some computable function of k.
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