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The generation of random, binary unordered trees

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Abstract

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.

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Authors and Affiliations

  1. Bell Communications Research, 445 South St., 07960, Morristown, NJ, USA

    George W. Furnas

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  1. George W. Furnas
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Additional information

This work was supported by the Alfred P. Sloan Foundation through the Center for Cognitive Science of The University of Texas at Austin, by Bell Communications Research, Inc., and by the Bell Laboratories. The author would like to thank W. H. E. Day for his extensive comments on an early draft of this manuscript, and K. E. Lochbaum for her help in programming and proofreading.

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Furnas, G.W. The generation of random, binary unordered trees. Journal of Classification 1, 187–233 (1984). https://doi.org/10.1007/BF01890123

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