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
Computing the minimum number of hybridization events for a consistent evolutionary history
Discrete Applied Mathematics
Computing the Hybridization Number of Two Phylogenetic Trees Is Fixed-Parameter Tractable
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Hybridization in Nonbinary Trees
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Computing galled networks from real data
Bioinformatics
Level-k Phylogenetic Networks Are Constructable from a Dense Triplet Set in Polynomial Time
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
The Structure of Level-k Phylogenetic Networks
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Constructing Level-2 Phylogenetic Networks from Triplets
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Beyond galled trees: decomposition and computation of galled networks
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
Phylogenetic networks do not need to be complex
Bioinformatics
Phylogenetic Networks: Concepts, Algorithms and Applications
Phylogenetic Networks: Concepts, Algorithms and Applications
Constructing a smallest refining galled phylogenetic network
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Fast computation of the exact hybridization number of two phylogenetic trees
ISBRA'10 Proceedings of the 6th international conference on Bioinformatics Research and Applications
A quadratic kernel for computing the hybridization number of multiple trees
Information Processing Letters
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Rooted phylogenetic networks are often used to represent conflicting phylogenetic signals. Given a set of clusters, a network is said to represent these clusters in the softwired sense if, for each cluster in the input set, at least one tree embedded in the network contains that cluster. Motivated by parsimony we might wish to construct such a network using as few reticulations as possible, or minimizing the level of the network, i.e., the maximum number of reticulations used in any "tangled” region of the network. Although these are NP-hard problems, here we prove that, for every fixed k \ge 0, it is polynomial-time solvable to construct a phylogenetic network with level equal to k representing a cluster set, or to determine that no such network exists. However, this algorithm does not lend itself to a practical implementation. We also prove that the comparatively efficient Cass algorithm correctly solves this problem (and also minimizes the reticulation number) when input clusters are obtained from two not necessarily binary gene trees on the same set of taxa but does not always minimize level for general cluster sets. Finally, we describe a new algorithm which generates in polynomial-time all binary phylogenetic networks with exactly r reticulations representing a set of input clusters (for every fixed r \ge 0).