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Solving the tree containment problem in linear time for nearly stable phylogenetic networks

Abstract : A phylogenetic network is a rooted acyclic digraph whose leaves are uniquely labeled with a set of taxa. The tree containment problem asks whether or not a phylogenetic network displays a phylogenetic tree over the same set of labeled leaves. It is a fundamental problem arising from validation of phylogenetic network models. The tree containment problem is NP-complete in general. To identify network classes on which the problem is polynomial time solvable, we introduce two classes of networks by generalizations of tree-child networks through vertex stability, namely nearly stable networks and genetically stable networks. Here, we study the combinatorial properties of these two classes of phylogenetic networks. We also develop a linear-time algorithm for solving the tree containment problem on binary nearly stable networks.
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Contributor : Philippe Gambette Connect in order to contact the contributor
Submitted on : Thursday, July 26, 2018 - 12:54:08 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM
Long-term archiving on: : Saturday, October 27, 2018 - 12:56:24 PM


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Philippe Gambette, Andreas D.M. Gunawan, Anthony Labarre, Stéphane Vialette, Louxin Zhang. Solving the tree containment problem in linear time for nearly stable phylogenetic networks. Discrete Applied Mathematics, 2018, 246, pp.62-79. ⟨10.1016/j.dam.2017.07.015⟩. ⟨hal-01575001⟩



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