Reconstruction of rooted trees from subtrees
Discrete Applied Mathematics
Determining the evolutionary tree using experiments
Journal of Algorithms
The difficulty of constructing a leaf-labelled tree including or avoiding given subtrees
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Efficient Reconstruction of Phylogenetic Networks with Constrained Recombination
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Reconstructing reticulate evolution in species: theory and practice
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Reconstructing Recombination Network from Sequence Data: The Small Parsimony Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Fast algorithms for computing the tripartition-based distance between phylogenetic networks
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Reconstructing an ultrametric galled phylogenetic network from a distance matrix
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Constructing a smallest refining galled phylogenetic network
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
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This paper considers the problem of determining whether a given set T of rooted triplets can be merged without conflicts into a galled phylogenetic network, and if so, constructing such a network. When the input T is dense, we solve the problem in O(|T|) time, which is optimal since the size of the input is Θ(|T|). In comparison, the previously fastest algorithm for this problem runs in O(|T|2) time. Next, we prove that the problem becomes NP-hard if extended to non-dense inputs, even for the special case of simple phylogenetic networks. We also show that for every positive integer n, there exists some set T of rooted triplets on n leaves such that any galled network can be consistent with at most 0.4883·|T| of the rooted triplets in T. On the other hand, we provide a polynomial-time approximation algorithm that always outputs a galled network consistent with at least a factor of 5/12 (0.4166) of the rooted triplets in T.