Upper Bounds on the Average Height of Random Binary Trees

TL;DR

This paper investigates the average height of random binary trees generated by leaf-centric sources, extending known results about binary search trees and providing bounds on their expected height.

Contribution

It generalizes previous work by Devroye, establishing bounds on the average height for a broader class of random binary trees.

Findings

Average height of random binary trees is bounded by functions of log n

Generalizes bounds from binary search trees to leaf-centric sources

Provides theoretical upper bounds on tree height

Abstract

We study the average height of random trees generated by leaf-centric binary tree sources as introduced by Zhang, Yang and Kieffer. A leaf-centric binary tree source induces for every $n \geq 2$ a probability distribution on the set of binary trees with $n$ leaves. Our results generalize a result by Devroye, according to which the average height of a random binary search tree of size $n$ is in $\mathcal{O}(\log n)$.