On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)
SIAM Journal on Computing
Improved non-approximability results for minimum vertex cover with density constraints
Theoretical Computer Science
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Maximum likelihood of evolutionary trees is hard
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Finding a maximum likelihood tree is hard
Journal of the ACM (JACM)
Distorted Metrics on Trees and Phylogenetic Forests
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Shrinkage Effect in Ancestral Maximum Likelihood
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Untangling Tanglegrams: Comparing Trees by Their Drawings
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
Phylogenies without Branch Bounds: Contracting the Short, Pruning the Deep
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Polynomial supertree methods revisited
PRIB'10 Proceedings of the 5th IAPR international conference on Pattern recognition in bioinformatics
Untangling Tanglegrams: Comparing Trees by Their Drawings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Learning Latent Tree Graphical Models
The Journal of Machine Learning Research
The Complexity of Finding Multiple Solutions to Betweenness and Quartet Compatibility
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Proceedings of the 27th Annual ACM Symposium on Applied Computing
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Hamiltonian Walks of Phylogenetic Treespaces
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Is the Protein Model Assignment problem under linked branch lengths NP-hard?
Theoretical Computer Science
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Maximum likelihood is one of the most widely used techniques to infer evolutionary histories. Although it is thought to be intractable, a proof of its hardness has been lacking. Here, we give a short proof that computing the maximum likelihood tree is NP-hard by exploiting a connection between likelihood and parsimony observed by Tuffley and Steel.