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Journal of Classification

, Volume 6, Issue 1, pp 223–231 | Cite as

Fast random generation of binary, t-ary and other types of trees

  • Adolfo J. Quiroz
Authors Of Artides

Abstract

Trees, and particularly binary trees, appear frequently in the classification literature. When studying the properties of the procedures that fit trees to sets of data, direct analysis can be too difficult, and Monte Carlo simulations may be necessary, requiring the implementation of algorithms for the generation of certain families of trees at random. In the present paper we use the properties of Prufer's enumeration of the set of completely labeled trees to obtain algorithms for the generation of completely labeled, as well as terminally labeled t-ary (and in particular binary) trees at random, i.e., with uniform distribution. Actually, these algorithms are general in that they can be used to generate random trees from any family that can be characterized in terms of the node degrees. The algorithms presented here are as fast as (in the case of terminally labeled trees) or faster than (in the case of completely labeled trees) any other existing procedure, and the memory requirements are minimal. Another advantage over existing algorithms is that there is no need to store pre-calculated tables.

Keywords

Tree algorithms Monte Carlo studies Clustering methodology 

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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Adolfo J. Quiroz
    • 1
  1. 1.Departamento de MatemáticasUniversidad Simón BolívarCaracasVenezuela

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