Level-k Phylogenetic Network can be Constructed from a Dense Triplet Set in Polynomial Time

Thu-Hien To (1) , Michel Habib (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

Given a dense triplet set $\mathcal{T}$, there arise two interesting questions: Does there exists any phylogenetic network consistent with $\mathcal{T}$? And if so, can we find an effective algorithm to construct one? For cases of networks of levels $k=0$ or $1$ or $2$, these questions were answered with effective polynomial algorithms. For higher levels $k$, partial answers were recently obtained with an $O(|\mathcal{T}|^{k+1})$ time algorithm for simple networks. In this paper we give a complete answer to the general case. The main idea is to use a special property of SN-sets in a level-k network. As a consequence, we can also find the level-k network with the minimum number of reticulations in polynomial time.

Mots clés: phylogenetic network; triplet

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Thu-Hien To, Michel Habib. Level-k Phylogenetic Network can be Constructed from a Dense Triplet Set in Polynomial Time. 2009. ⟨hal-00352360⟩