Phylogenetic Network Diversity Parameterized by Reticulation Number and Beyond

Leo van Iersel; Mark Jones; Jannik Schestag; Celine Scornavacca; Mathias Weller

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arXiv · 2405.01091

Phylogenetic Network Diversity Parameterized by Reticulation Number and Beyond

Leo van Iersel·Mark Jones·Jannik Schestag·Celine Scornavacca·Mathias Weller

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Abstract

Network Phylogenetic Diversity (Network-PD) is a measure for the diversity of a set of species based on a rooted phylogenetic network (with branch lengths and inheritance probabilities on the reticulation edges) describing the evolution of those species. We consider the Max-Network-PD problem: Given such a network, find k species with maximum Network-PD score. We show that this problem is fixed-parameter tractable (FPT) for binary networks, by describing an optimal algorithm running in O(2r log(k)(n + r)) time, with n the total number of species in the network and r its reticulation number. Furthermore, we show that Max-Network-PD is NP-hard for level-1 networks, proving that, unless P=NP, the FPT approach cannot be extended by using the level as parameter instead of the reticulation number.

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Leo van Iersel, Mark Jones, Jannik Schestag, Celine Scornavacca, Mathias Weller. 2024-05-02. Phylogenetic Network Diversity Parameterized by Reticulation Number and Beyond. https://arxiv.org/abs/2405.01091

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