Computational complexity of inferring phylogenies from dissimilarity matrices
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Molecular biologists strive to infer evolutionary relationships from quantitative macromolecular comparisons obtained by immunological, DNA hybridization, electrophoretic or amino acid sequencing techniques. The problem is to find unrooted phylogenies that best approximate a given dissimilarity matrix according to a goodness-of-fit measure, for example the least-squares-fit criterion or Farris'sf statistic. Computational costs of known algorithms guaranteeing optimal solutions to these problems increase exponentially with problem size; practical computational considerations limit the algorithms to analyzing small problems. It is established here that problems of phylogenetic inference based on the least-squares-fit criterion and thef statistic are NP-complete and thus are so difficult computationally that efficient optimal algorithms are unlikely to exist for them.
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- Buneman, P. 1971. “The Recovery of Trees from Measures of Dissimilarity”. InMathematics in the Archaeological and Historical Sciences, F. R. Hodson, D. G. Kendall and P. Tautu (Eds), pp. 387–395. Edinburgh: Edinburgh University Press.Google Scholar
- Cavalli-Sforza, L. L. and A. W. F. Edwards. 1965. “Analysis of Human Evolution.” InGenetics Today: Proceedings of the XI International Congress of Genetics, Vol. 3, S. J. Geerts (Ed.), pp. 923–933. Oxford: Pergamon Press.Google Scholar
- — and —. 1967. “Phylogenetic Analysis: Models and Estimation Procedures”.Am. J. hum. Genet. 19, 233–257;Evolution 21, 550–570.Google Scholar
- —.1981. “Distance Data in Phylogenetic Analysis”. InAdvances in Cladistics: Proceedings of the First Meeting of the Willi Hennig Society, V. A. Funk and D. R. Brooks (Eds), pp. 3–23. Bronx: New York Botanical Garden.Google Scholar
- Fitch, W. M. and E. Margoliash. 1967. “Construction of Phylogenetic Trees”.Science 155, 279–284.Google Scholar
- Garey, M. R. and D. S. Johnson. 1979.Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco: W. H. Freeman.Google Scholar
- Harary, F. 1969Graph Theory. Reading, Massachusetts: Addison-Wesley.Google Scholar
- Jardine, N. and R. Sibson.Mathematical Taxonomy. London: John Wiley.Google Scholar
- Křivánek, M. 1986. “On the Computational Complexity of Clustering.” InData Analysis and Informatics IV, E. Didayet al. (Eds), pp. 89–96. Amsterdam: Elsevier Science.Google Scholar
- — and J. Morávek. 1984. “On NP-hardness in Hierarchical Clustering.” InCompstat 1984, T. Havránek, Z. Šidák and M. Novák (Eds), pp. 189–194. Wien: Physica-Verlag.Google Scholar