Journal of Classification

, Volume 1, Issue 1, pp 187–233 | Cite as

The generation of random, binary unordered trees

  • George W. Furnas
Authors Of Articles


Several techniques are given for the uniform generation of trees for use in Monte Carlo studies of clustering and tree representations. First, general strategies are reviewed for random selection from a set of combinatorial objects with special emphasis on two that use random mapping operations. Theorems are given on how the number of such objects in the set (e.g., whether the number is prime) affects which strategies can be used. Based on these results, methods are presented for the random generation of six types of binary unordered trees. Three types of labeling and both rooted and unrooted forms are considered. Presentation of each method includes the theory of the method, the generation algorithm, an analysis of its computational complexity and comments on the distribution of trees over which it samples. Formal proofs and detailed algorithms are in appendices.


Uniform sampling Tree construction Monte Carlo studies Tree algorithms Clustering methodology Classification methodology 


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • George W. Furnas
    • 1
  1. 1.Bell Communications ResearchMorristownUSA

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