Computing a smallest multi-labeled phylogenetic tree from rooted triplets

Abstract

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