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Growing random uniform d-ary trees

Abstract : Let T d (n) be the set of d-ary rooted trees with n internal nodes. We give a method to construct a sequence (t n , n ≥ 0) where, for any n ≥ 1, t n has the uniform distribution in T d (n), and t n is constructed from t n−1 by the addition of a new node, and a rearrangement of the structure of t n−1. This method is inspired by Rémy's algorithm which does this job in the binary case, but it is different from it. This provides a method for the random generation of a uniform d-ary tree in T d (n) with a cost linear in n.
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Preprints, Working Papers, ...
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Contributor : Jean-François Marckert <>
Submitted on : Tuesday, May 11, 2021 - 8:50:08 AM
Last modification on : Friday, June 4, 2021 - 3:35:43 AM


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  • HAL Id : hal-03223472, version 1
  • ARXIV : 2105.05513



Jean-Francois Marckert, Luis Fredes Carrasco. Growing random uniform d-ary trees. 2021. ⟨hal-03223472⟩