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Computing a Smallest Multilabeled Phylogenetic Tree from Rooted Triplets

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3 Author(s)
Guillemot, S. ; Inst. Gaspard Monge, Univ. Paris-Est, Marne-la-Vallee, France ; Jansson, J. ; Wing-Kin Sung

We investigate the computational complexity of inferring a smallest possible multilabeled phylogenetic tree (MUL tree) which is consistent with each of the rooted triplets in a given set. This problem has not been studied previously in the literature. We prove that even the very restricted case of determining if there exists a MUL tree consistent with the input and having just one leaf duplication is an NP-hard problem. Furthermore, we showthatthe general minimization problem is difficult to approximate, although a simple polynomial-time approximation algorithm achieves an approximation ratio close to our derived inapproximability bound. Finally, we provide an exact algorithm for the problem running in exponential time and space. As a by-product, we also obtain new, strong inapproximability results for two partitioning problems on directed graphs called Acyclic Partition and Acyclic Tree-Partition.

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Computational Biology and Bioinformatics, IEEE/ACM Transactions on  (Volume:8 ,  Issue: 4 )