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Kernelizations for the hybridization number problem on multiple nonbinary trees

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

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