Phylogenetic Network Diversity Parameterized by Reticulation Number and Beyond
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.
Keywords
Cite
@article{arxiv.2405.01091,
title = {Phylogenetic Network Diversity Parameterized by Reticulation Number and Beyond},
author = {Leo van Iersel and Mark Jones and Jannik Schestag and Celine Scornavacca and Mathias Weller},
journal= {arXiv preprint arXiv:2405.01091},
year = {2025}
}