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

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

2009-01-12

arxiv.org/abs/0901.1657v1

Biology

Quantitative Biology

Populations and Evolution

Scientific paper

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.

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