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arXiv · 1311.4045

Kernelizations for the hybridization number problem on multiple nonbinary trees

Leo van Iersel·Steven Kelk·Celine Scornavacca
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Abstract

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 $4k(5k)^t$ 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 these 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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Leo van Iersel, Steven Kelk, Celine Scornavacca. 2013-11-16. Kernelizations for the hybridization number problem on multiple nonbinary trees. https://arxiv.org/abs/1311.4045

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