Abstract
The \(\mathcal {R}^{+-} \mathcal {F}^{+-}\) Consistency problem takes as input two sets \(R^{+}\) and \(R^{-}\) of resolved triplets and two sets \(F^{+}\) and \(F^{-}\) of fan triplets, and asks for a distinctly leaf-labeled tree that contains all elements in \(R^{+} \cup F^{+}\) and no elements in \(R^{-} \cup F^{-}\) as embedded subtrees, if such a tree exists. This paper presents a detailed characterization of how the computational complexity of the problem changes under various restrictions. Our main result is an efficient algorithm for dense inputs satisfying \(R^{-} = \emptyset \) whose running time is linear in the size of the input and therefore optimal.
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Acknowledgments
The authors would like to thank Sylvain Guillemot and Avraham Melkman for some discussions related to the topic of this paper. J.J. was partially funded by The Hakubi Project at Kyoto University and KAKENHI grant number 26330014.
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Jansson, J., Lingas, A., Rajaby, R., Sung, WK. (2017). Determining the Consistency of Resolved Triplets and Fan Triplets. In: Sahinalp, S. (eds) Research in Computational Molecular Biology. RECOMB 2017. Lecture Notes in Computer Science(), vol 10229. Springer, Cham. https://doi.org/10.1007/978-3-319-56970-3_6
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