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A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood Is Hard
January-March 2006 (vol. 3 no. 1)
pp. 92-94
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.

[1] L. Addario-Berry, B. Chor, M.T. Hallett, J. Lagergren, A. Panconesi, and T. Wareham, “Ancestral Maximum Likelihood of Evolutionary Trees is Hard,” J. Bioinformatics and Computational Biology, vol. 2, no. 2, pp. 257-271, 2004.
[2] R. Agarwala, V. Bafna, M. Farach, B. Narayanan, M. Paterson, and M. Thorup, “On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics),” SIAM J. Computing, vol. 28, pp. 1073-1085, 1999.
[3] G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi, Complexity and Approximation. Berlin: Springer, 1999.
[4] J. Cavender, “Taxonomy with Confidence,” Math. Biosciences, vol. 40, pp. 271-280, 1978.
[5] B. Chor and T. Tuller, “Maximum Likelihood of Evolutionary Trees is Hard,” Proc. Ninth Int'l Conf. Computational Molecular Biology (RECOMB 2005), 2005.
[6] A. Clementi and L. Trevisan, “Improved Non-Approximability Results for Minimum Vertex Cover with Density Constraints,” Theoretical Computer Science, vol. 225, nos. 1-2, pp. 113-128, 1999.
[7] W. Day, D. Jonhson, and D. Sankoff, “The Computational Complexity of Inferring Rooted Phylogenies by Parsimony,” Math. Biosciences, vol. 81, pp. 33-42, 1986.
[8] W. Day and D. Sankoff, “The Computational Complexity of Inferring Phylogenies by Compatibility,” Systematic Zoology, vol. 35, pp. 224-229, 1986.
[9] A.W.F. Edwards and L.L. Cavalli-Sforza, “Reconstruction of Evolutionary Trees,” Phenetic and Phylogenetic Classification, V.H. Heywood and J. McNeill, eds. Systematics Assoc., London, vol. 6, pp. 67-76, 1964.
[10] J.S. Farris, “A Probability Model for Inferring Evolutionary Trees,” Systematic Zoology, vol. 22, pp. 250-256, 1973.
[11] J. Felsenstein, “Evolutionary Trees from DNA Sequences: A Maximum Likelihood Approach,” J. Molecular Evolution, vol. 17, pp. 368-376, 1981.
[12] J. Felsenstein, Inferring Phylogenies. Sunderland: Sinauer Assoc., 2004.
[13] L. Foulds and R. Graham, “The Steiner Problem in Phylogeny is NP-Complete,” Advances in Applied Math., vol. 3, pp. 43-49, 1982.
[14] M.R. Garey and D.S. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness, San Francisco: W.H. Freeman, 1976.
[15] J. Neyman, “Molecular Studies of Evolution: A Source of Novel Statistical Problems,” Statistical Decision Theory and Related Topics, S.S. Gupta and J. Yackel, eds. New York: Academic Press, pp. 1-27, 1971.
[16] C. Semple and M. Steel, Phylogenetics. Oxford Univ. Press, 2003.
[17] C. Tuffley and M. Steel, “Links between Maximum Likelihood and Maximum Parsimony under a Simple Model of Site Substitution,” Bull. Math. Biology, vol. 59, no. 3, pp. 581-607, 1997.
[18] H.T. Wareham, On the Computational Complexity of Inferring Evolutionary Trees, MSc thesis, Technical Report no. 9301, Dept. of Computer Science, Memorial Univ. of Newfoundland 1993.

Index Terms:
Analysis of algorithms and problem complexity, probability and statistics, biology and genetics.
Sebastien Roch, "A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood Is Hard," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. 1, pp. 92-94, Jan.-March 2006, doi:10.1109/TCBB.2006.4
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