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Kernelizations for the hybridization number problem on multiple nonbinary trees. (English) Zbl 1342.68170
Summary: Given a finite set \(X\), a collection \(\mathcal{T}\) 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 \(\mathcal{T}\) and has reticulation number at most \(k\). We show two kernelization algorithms for Hybridization Number, with kernel sizes \(4 k(5 k)^t\) and \(20 k^2({\Delta}^+ - 1)\) 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 \(n = | X |\) and \(f\) some computable function of \(k\).

68Q25 Analysis of algorithms and problem complexity
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
92D15 Problems related to evolution
Full Text: DOI
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