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

Author

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  • Martin Frohn

    (Maastricht University)

  • Steven Kelk

    (Maastricht University)

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.

Suggested Citation

  • Martin Frohn & Steven Kelk, 2025. "A 2-approximation algorithm for the softwired parsimony problem on binary, tree-child phylogenetic networks," Annals of Operations Research, Springer, vol. 345(1), pages 125-145, February.
    • Handle: RePEc:spr:annopr:v:345:y:2025:i:1:d:10.1007_s10479-024-06452-0
    DOI: 10.1007/s10479-024-06452-0
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