Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
On the complexity of comparing evolutionary trees
Discrete Applied Mathematics - Special volume on computational molecular biology
Computing the Hybridization Number of Two Phylogenetic Trees Is Fixed-Parameter Tractable
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A 3-approximation algorithm for the subtree distance between phylogenies
Journal of Discrete Algorithms
Summarizing Multiple Gene Trees Using Cluster Networks
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Hybridization in Nonbinary Trees
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Metrics for Phylogenetic Networks I: Generalizations of the Robinson-Foulds Metric
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Drawing Rooted Phylogenetic Networks
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Rotation distance is fixed-parameter tractable
Information Processing Letters
Efficiently Calculating Evolutionary Tree Measures Using SAT
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Comparison of Tree-Child Phylogenetic Networks
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Accurate computation of likelihoods in the coalescent with recombination via parsimony
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
A unifying view on approximation and FPT of agreement forests
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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)
Optimizing Phylogenetic Networks for Circular Split Systems
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
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 practical approximation algorithm for solving massive instances of hybridization number
WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics
On the complexity of computing the temporal hybridization number for two phylogenies
Discrete Applied Mathematics
An algorithm for constructing parsimonious hybridization networks with multiple phylogenetic trees
RECOMB'13 Proceedings of the 17th international conference on Research in Computational Molecular Biology
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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It is now well-documented that the structure of evolutionary relationships between a set of present-day species is not necessarily tree-like. The reason for this is that reticulation events such as hybridizations mean that species are a mixture of genes from different ancestors. Since such events are relatively rare, a fundamental problem for biologists is to determine the smallest number of hybridization events required to explain a given (input) set of data in a single (hybrid) phylogeny. The main results of this paper show that computing this smallest number is APX-hard, and thus NP-hard, in the case the input is a collection of phylogenetic trees on sets of present-day species. This answers a problem which was raised at a recent conference (Phylogenetic Combinatorics and Applications, Uppsala University, 2004). As a consequence of these results, we also correct a previously published NP-hardness proof in the case the input is a collection of binary sequences, where each sequence represents the attributes of a particular present-day species. The APX-hardness of these problems means that it is unlikely that there is an efficient algorithm for either computing the result exactly or approximating it to any arbitrary degree of accuracy.