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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.
Analysis of algorithms and problem complexity, probability and statistics, biology and genetics.

S. Roch, "A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood Is Hard," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. , pp. 92-94, 2006.
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