Computational complexity of inferring phylogenies from dissimilarity matrices
 William H. E. Day
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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 goodnessoffit measure, for example the leastsquaresfit 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 leastsquaresfit criterion and thef statistic are NPcomplete and thus are so difficult computationally that efficient optimal algorithms are unlikely to exist for them.
 Bandelt, H.J. and A. Dress. 1986. “Reconstructing the Shape of a Tree from Observed Dissimilarity Data”.Adv. appl. Math. 7, 309–343. CrossRef
 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.
 CavalliSforza, 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.
 — and —. 1967. “Phylogenetic Analysis: Models and Estimation Procedures”.Am. J. hum. Genet. 19, 233–257;Evolution 21, 550–570.
 Day, W. H. E. 1983. “Computationally Difficult Parsimony Problems in Phylogenetic Systematics”.J. theor. Biol. 103, 429–438. CrossRef
 —, D. S. Johnson and D. Sankoff. 1986. “The Computational Complexity of Inferring Rooted Phylogenies by Parsimony”.Math. Biosci. 81, 33–42. CrossRef
 — and D. Sankoff. 1986. “Computational Complexity of Inferring Phylogenies by Compatibility”.Syst. Zool. 35, 224–229. CrossRef
 — and —. 1987. “Computational Complexity of Inferring Phylogenies from Chromosome Inversion Data”.J. theor. Biol. 124, 213–218. CrossRef
 Dobson, A. J. 1974. “Unrooted Trees for Numerical Taxonomy”.J. appl. Probab. 11, 32–42. CrossRef
 Farris, J. S. 1972. “Estimating Phylogenetic Trees from Distance Matrices”.Am. Nat. 106, 645–668. CrossRef
 —.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.
 Fitch, W. M. and E. Margoliash. 1967. “Construction of Phylogenetic Trees”.Science 155, 279–284.
 Foulds, L. R. and R. L. Graham. 1982. “The Steiner Problem in Phylogeny is NPcomplete”.Adv. appl. Math. 3, 43–49. CrossRef
 Garey, M. R. and D. S. Johnson. 1979.Computers and Intractability: A Guide to the Theory of NPCompleteness. San Francisco: W. H. Freeman.
 Graham, R. L. and L. R. Foulds. 1982. “Unlikelihood that Minimal Phylogenies for a Realistic Biological Study can be Constructed in Reasonable Computational Time”.Math. Biosci. 60, 133–142. CrossRef
 Hakimi, S. L. and S. S. Yau. 1965. “Distance Matrix of a Graph and its Realizability.”Quart. appl. Math. 22, 305–317.
 Harary, F. 1969Graph Theory. Reading, Massachusetts: AddisonWesley.
 Hartigan, J. A. 1967. “Representation of Similarity Matrices by Trees”.J. Am. Statist. Ass. 62, 1140–1158. CrossRef
 Jardine, N. and R. Sibson.Mathematical Taxonomy. London: John Wiley.
 Křivánek, M. 1986. “On the Computational Complexity of Clustering.” InData Analysis and Informatics IV, E. Didayet al. (Eds), pp. 89–96. Amsterdam: Elsevier Science.
 — and J. Morávek. 1984. “On NPhardness in Hierarchical Clustering.” InCompstat 1984, T. Havránek, Z. Šidák and M. Novák (Eds), pp. 189–194. Wien: PhysicaVerlag.
 — and —. 1986. “NPhard Problems in Hierarchicaltree Clustering.”Acta Inform. 23, 311–323. CrossRef
 Prager, E. M. and A. C. Wilson. 1976. “Congruency of Phylogenies Derived from Different Proteins.”J. mol. Evol. 9, 45–57. CrossRef
 Sattath, S. and A. Tversky. 1977. “Additive Similarity Trees.”Psychometrika 42, 319–345. CrossRef
 Title
 Computational complexity of inferring phylogenies from dissimilarity matrices
 Journal

Bulletin of Mathematical Biology
Volume 49, Issue 4 , pp 461467
 Cover Date
 19870701
 DOI
 10.1007/BF02458863
 Print ISSN
 00928240
 Online ISSN
 15229602
 Publisher
 Kluwer Academic Publishers
 Additional Links
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 Industry Sectors
 Authors

 William H. E. Day ^{(1)}
 Author Affiliations

 1. Department of Computer Science, Memorial University of Newfoundland, A1C 5S7, St. John's, Newfoundland, Canada