Computing a Smallest Multi-labeled Phylogenetic Tree from Rooted Triplets

Authors:
Sylvain Guillemot;Jesper Jansson;Wing-Kin Sung
Affiliations:
Institut Gaspard Monge, Université Paris-Est, Marne-la-Vallée, France 77454;Ochanomizu University, Tokyo, Japan 112-8610;School of Computing, National University of Singapore, Singapore 117543 and Genome Institute of Singapore, Genome, Singapore 138672
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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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 驴驴 for any constant 0 驴 ≤ 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.