A note on the height of binary search trees
Journal of the ACM (JACM)
Branching processes in the analysis of the heights of trees
Acta Informatica
Distances in random plane-oriented recursive trees
Journal of Computational and Applied Mathematics - Special issue on asymptotic methods in analysis and combinatorics
On the Variance of the Height of Random Binary Search Trees
SIAM Journal on Computing
The strong convergence of maximal degrees in uniform random recursive trees and dags
Random Structures & Algorithms
On the Depth of Randomly Generated Circuits
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Total Path Length for Random Recursive Trees
Combinatorics, Probability and Computing
On the Expected Depth of Random Circuits
Combinatorics, Probability and Computing
Random Trees: An Interplay between Combinatorics and Probability
Random Trees: An Interplay between Combinatorics and Probability
Note on the heights of random recursive trees and random m‐ary search trees
Random Structures & Algorithms
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We study depth properties of a general class of random recursive trees where each node i attaches to the random node \documentclass{article} \usepackage{mathrsfs, amsmath, amssymb}\pagestyle{empty} \begin{document} \begin{align*}\left\lfloor iX_i\right\rfloor\end{align*} \end{document} **image** and X0,…,Xn is a sequence of i.i.d. random variables taking values in [0,1). We call such trees scaled attachment random recursive trees (sarrt). We prove that the typical depth Dn, the maximum depth (or height) Hn and the minimum depth Mn of a sarrt are asymptotically given by Dn ∼μ-1 log n, Hn ∼ αmax log n and Mn ∼ αmin log n where μ,αmax and αmin are constants depending only on the distribution of X0 whenever X0 has a density. In particular, this gives a new elementary proof for the height of uniform random recursive trees Hn ∼ elog n that does not use branching random walks.© 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011, © 2012 Wiley Periodicals, Inc. (Supported by an NSERC Discovery Grant program.)