Making a Network Orchard by Adding Leaves
L.J.J. Van Iersel (TU Delft - Discrete Mathematics and Optimization)
Mark Jones (TU Delft - Discrete Mathematics and Optimization)
Esther Julien (TU Delft - Discrete Mathematics and Optimization)
Yukihiro Murakami (TU Delft - Discrete Mathematics and Optimization)
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Abstract
Phylogenetic networks are used to represent the evolutionary history of species. Recently, the new class of orchard networks was introduced, which were later shown to be interpretable as trees with additional horizontal arcs. This makes the network class ideal for capturing evolutionary histories that involve horizontal gene transfers. Here, we study the minimum number of additional leaves needed to make a network orchard. We demonstrate that computing this proximity measure for a given network is NP-hard and describe a tight upper bound. We also give an equivalent measure based on vertex labellings to construct a mixed integer linear programming formulation. Our experimental results, which include both real-world and synthetic data, illustrate the efficiency of our implementation.
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