Growing random uniform d-ary trees
Combinatorics
2021-05-13 v1 Probability
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 R{\'e}my'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.
Keywords
Cite
@article{arxiv.2105.05513,
title = {Growing random uniform d-ary trees},
author = {Jean-Francois Marckert},
journal= {arXiv preprint arXiv:2105.05513},
year = {2021}
}