Computing a Smallest Multi-labeled Phylogenetic Tree from Rooted Triplets
We investigate the computational complexity of a new combinatorial problem of inferring a smallest possible multi-labeled phylogenetic tree (MUL tree) which is consistent with each of the rooted triplets in a given set. We prove that even the restricted case of determining if there exists a MUL tree consistent with the input and having just one leaf duplication is NP-hard. Furthermore, we show that the general minimization problem is NP-hard to approximate within a ratio of n 1 − ε for any constant 0 < ε ≤ 1, where n denotes the number of distinct leaf labels in the input set, although a simple polynomial-time approximation algorithm achieves the approximation ratio n. We also provide an exact algorithm for the problem running in O *(7 n ) time and O *(3 n ) space.
KeywordsDirected Graph Internal Node Chromatic Number Phylogenetic Network Lower Common Ancestor
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- 4.Chen, J., Liu, Y., Lu, S., O’Sullivan, B., Razgon, I.: A fixed-parameter algorithm for the directed feedback vertex set problem (Article 21). Journal of the ACM 55(5) (2008)Google Scholar