A 2-approximation algorithm for the softwired parsimony problem on binary, tree-child phylogenetic networks

Martin Frohn; Steven Kelk

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arXiv · 2409.18077

A 2-approximation algorithm for the softwired parsimony problem on binary, tree-child phylogenetic networks

Martin Frohn·Steven Kelk

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Abstract

Finding the most parsimonious tree inside a phylogenetic network with respect to a given character is an NP-hard combinatorial optimization problem that for many network topologies is essentially inapproximable. In contrast, if the network is a rooted tree, then Fitch's well-known algorithm calculates an optimal parsimony score for that character in polynomial time. Drawing inspiration from this we here introduce a new extension of Fitch's algorithm which runs in polynomial time and ensures an approximation factor of 2 on binary, tree-child phylogenetic networks, a popular topologically-restricted subclass of phylogenetic networks in the literature. Specifically, we show that Fitch's algorithm can be seen as a primal-dual algorithm, how it can be extended to binary, tree-child networks and that the approximation guarantee of this extension is tight. These results for a classic problem in phylogenetics strengthens the link between polyhedral methods and phylogenetics and can aid in the study of other related optimization problems on phylogenetic networks.

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Martin Frohn, Steven Kelk. 2024-09-26. A 2-approximation algorithm for the softwired parsimony problem on binary, tree-child phylogenetic networks. https://arxiv.org/abs/2409.18077

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