Orienting undirected phylogenetic networks
Katharina T. Huber (University of East Anglia)
Leo van Iersel (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Remie Janssen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Mark Jones (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Vincent Moulton (University of East Anglia, Discrete Mathematics and Optimization)
Yukihiro Murakami (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Charles Semple (University of Canterbury)
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Abstract
This paper studies the relationship between undirected (unrooted) and directed (rooted) phylogenetic networks. We describe a polynomial-time algorithm for deciding whether an undirected nonbinary phylogenetic network, given the locations of the root and reticulation vertices, can be oriented as a directed nonbinary phylogenetic network. Moreover, we characterize when this is possible and show that, in such instances, the resulting directed nonbinary phylogenetic network is unique. In addition, without being given the location of the root and the reticulation vertices, we describe an algorithm for deciding whether an undirected binary phylogenetic network N can be oriented as a directed binary phylogenetic network of a certain class. The algorithm is fixed-parameter tractable (FPT) when the parameter is the level of N and is applicable to classes of directed phylogenetic networks that satisfy certain conditions. As an example, we show that the well-studied class of binary tree-child networks satisfies these conditions.
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