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An algorithm to equiprobably generate all directed trees withk labeled terminal nodes and unlabeled interior nodes

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Abstract

A computer algorithm is presented which equiprobably generates any member of the set of all directed trees withk labeled terminal nodes and unlabeled interior nodes. The algorithm requires roughlyk 2/2 storage locations. The one-time initialization requiresO(k 2) time, while generating each tree requiresO(k) time.

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Literature

  • Edwards, A. W. F. and L. L. Cavalli-Sforza. 1964. “Reconstruction of Evolutionary Trees.” InPhenetic and Phylogenetic Classification, Eds. W. H. Heywood and J. McNeill, Systematics Association Publication Number 6, pp. 67–76. London.

  • Felsenstein, J. 1978. “The Number of Evolutionary Trees.”Syst. Zool. 27, 27–33.

    Article  Google Scholar 

  • Foulds, L. R. and R. W. Robinson. 1981.Enumeration of Binary Phylogenetic Trees, Lecture Notes in Mathematics, No. 884. pp. 173–186. New York: Springer-Verlag.

    Google Scholar 

  • Knuth, D. E. 1973.The Art of Computer Programming. Vol. 1, 2nd Edn. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Knott, G. D. 1977. “A Numbering System for Binary Trees.”Communs Ass. comput. Mach. 20, 113–115.

    MATH  Google Scholar 

  • Leclerc, B. 1982.Description, Evaluation et Comparison des Hierarchies de Parties. Paris: Centre d'Analyse et de Mathematique Sociale.

    Google Scholar 

  • Mickevich, M. F. 1978. “Taxonomic Congurence.”Syst. Zool. 27, 143–158.

    Article  Google Scholar 

  • Nijenhuis, A. and H. S. Wif. 1975. “Combinatorial Algorithms.” InComputer Science and Applied Mathematics, Ed. W. Rheinboldt, Ch. 24–25. New York: Academic Press.

    Google Scholar 

  • Penny, D., L. R. Fould and M. D. Hendy 1982. “Testing the Theory of Evolution by Comparing Phylogenetic Trees Constructed from Five Different Protein Sequences.”Nature 297, 197–200.

    Article  Google Scholar 

  • Proskurowski, A. 1980. “On the Generation of Binary Trees.”J. Ass. comput. Mach. 27, 1–2.

    MathSciNet  Google Scholar 

  • Rohlf, F. J. 1983. “Numbering Binary Trees with Labelled Terminal Vertices.”Bull. math. Biol. 45, 33–40.

    Article  MATH  MathSciNet  Google Scholar 

  • Schuh, R. J. and F. J. Farris 1981. “Methods for Investigating Taxonomic Congruence and their Application to the Leptopodomorpha.”Syst. Zool. 30, 331–350.

    Article  Google Scholar 

  • Shao, K. and F. J. Rohlf. 1983. “Sampling Distribution of Consensus Indices when all Bifurcating Trees are Equally Likely.” InNumerical Taxonomy. Proceedings of the NATO Advanced Study Institute, Ed. J. Felsenstein, pp. 132–137. NATO Advanced Study Institute Series G (Ecological Science), No. 1. New York: Springer-Verlag.

    Google Scholar 

  • Sokal, R. R. and F. J. Rohlf. 1981. “Taxonomic Congruence in the Leptopodomorpha Re-examined.”Syst. Zool. 30, 309–325.

    Article  Google Scholar 

  • Solomon, M. and R. A. Finkel. 1980. “A Note on Enumerating Binary Trees.”J. Ass. comput. Mach. 27, 3–5.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Ecology and Evolution, State University of New York at Stony Brook, 11794, Stony Brook, NY, USA

    Neal L. Oden & Kwang-Tsao Shao

Authors
  1. Neal L. Oden
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  2. Kwang-Tsao Shao
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Additional information

Contribution No. 477 in Ecology and Evolution, State University of New York at Stony Brook. This research was supported by Grant No. DEB8003508 from the National Science Foundation to Robert R. Sokal.

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Oden, N.L., Shao, KT. An algorithm to equiprobably generate all directed trees withk labeled terminal nodes and unlabeled interior nodes. Bltn Mathcal Biology 46, 379–387 (1984). https://doi.org/10.1007/BF02462013

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  • DOI: https://doi.org/10.1007/BF02462013

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