Level-k Phylogenetic Network can be Constructed from a Dense Triplet Set in Polynomial Time
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2009
- DOI:
- 10.48550/arXiv.0901.1657
- arXiv:
- arXiv:0901.1657
- Bibcode:
- 2009arXiv0901.1657T
- Keywords:
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- Quantitative Biology - Populations and Evolution