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 n1− for any constant 0 < ≤ 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∗ (7n ) time and O∗ (3n ) space.

• Type: Conference
• Year: 2009
• Where: ISAAC
• Authors: Sylvain Guillemot, Jesper Jansson, Wing-Kin Sung
• Keywords: Algorithms, ISAAC 2009, MUL Tree, Multi-labeled Phylogenetic Tree, Polynomial-time Approximation Algorithm