Abstract
We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is N based on T? We show that it is \(\textit{NP}\)-hard to decide, by reduction from 3-Dimensional Matching (3DM) and further that the problem is fixed-parameter tractable.
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Acknowledgments
We would like to thank the American Museum of Natural History and the CUNY Advanced Science Research Center for hosting us for several meetings. This work was funded by a Research Experience for Undergraduates (REU) Grant from the US National Science Foundation (#1461094 to St. John and Owen).
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Anaya, M., Anipchenko-Ulaj, O., Ashfaq, A. et al. On Determining if Tree-based Networks Contain Fixed Trees. Bull Math Biol 78, 961–969 (2016). https://doi.org/10.1007/s11538-016-0169-x
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DOI: https://doi.org/10.1007/s11538-016-0169-x