We consider the NP-hard Tree Containment problem that has important applications in phylogenetics. The problem asks if a given single-rooted leaf-labeled network (“phylogenetic network”) N “contains” a given leaf-labeled tree (“phylogenetic tree”) T. We develop a fast algorithm for the case that N is a phylogenetic tree in which multiple leaves might share a label. Generalizing a previously known decomposition scheme lets us leverage this algorithm, yielding linear-time algorithms for so-called “reticulation visible” networks and“nearly stable” networks. While these are special classes of networks, they rank among the most general of the previously considered cases. We also present a dynamic programming algorithm that solves the general problem in (Forumamal Presented). time, where the parameter t* is the maximum number of “tree components with unstable roots” in any block of the input network. Notably, t* is stronger (that is, smaller on all networks) than the previously considered parameter “number of reticulations” and even the popular parameter “level” of the input network.
CITATION STYLE
Weller, M. (2018). Linear-time tree containment in phylogenetic networks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11183 LNBI, pp. 309–323). Springer Verlag. https://doi.org/10.1007/978-3-030-00834-5_18
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