Computing the maximum agreement of phylogenetic networks
Theoretical Computer Science - Pattern discovery in the post genome
Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network
SIAM Journal on Computing
Inferring a level-1 phylogenetic network from a dense set of rooted triplets
Theoretical Computer Science - Computing and combinatorics
Constructing the Simplest Possible Phylogenetic Network from Triplets
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Constructing level-2 phylogenetic networks from triplets
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
The Structure of Level-k Phylogenetic Networks
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
On the Elusiveness of Clusters
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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For a given dense triplet set $\mathcal{T}$, there exist two natural questions [7]: Does there exist any phylogenetic network consistent with $\mathcal{T}$? In case such networks exist, can we find an effective algorithm to construct one? For cases of networks of levels k = 0, 1 or 2, these questions were answered in [1,6,7,8,10] with effective polynomial algorithms. For higher levels k , partial answers were recently obtained in [11] with an $O(|\mathcal{T}|^{k+1})$ time algorithm for simple networks. In this paper, we give a complete answer to the general case, solving a problem proposed in [7]. The main idea of our proof is to use a special property of SN-sets in a level-k network. As a consequence, for any fixed k , we can also find a level-k network with the minimum number of reticulations, if one exists, in polynomial time.