On the complexity of comparing evolutionary trees
Discrete Applied Mathematics - Special volume on computational molecular biology
Efficient algorithms for lateral gene transfer problems
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Computing the minimum number of hybridization events for a consistent evolutionary history
Discrete Applied Mathematics
A fundamental decomposition theory for phylogenetic networks and incompatible characters
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
A 3-approximation algorithm for the subtree distance between phylogenies
Journal of Discrete Algorithms
Hybridization in Nonbinary Trees
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Maximum Parsimony for Tree Mixtures
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A unifying view on approximation and FPT of agreement forests
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Algorithms for Reticulate Networks of Multiple Phylogenetic Trees
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
On the Elusiveness of Clusters
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Fast FPT algorithms for computing rooted agreement forests: theory and experiments
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
A quadratic kernel for computing the hybridization number of multiple trees
Information Processing Letters
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Reticulation processes in evolution mean that the ancestral history of certain groups of present-day species is non-tree-like. These processes include hybridization, lateral gene transfer, and recombination. Despite the existence of reticulation, such events are relatively rare and so a fundamental problem for biologists is the following: given a collection of rooted binary phylogenetic trees on sets of species that correctly represent the tree-like evolution of different parts of their genomes, what is the smallest number of "reticulation" vertices in any network that explains the evolution of the species under consideration. It has been previously shown that this problem is NP-hard even when the collection consists of only two rooted binary phylogenetic trees. However, in this paper, we show that the problem is fixed-parameter tractable in the two-tree instance, when parameterized by this smallest number of reticulation vertices.