On the silhouette of binary search trees

TL;DR

This paper studies the silhouette of binary search trees, which is a function on the unit interval derived from binary search tree paths, and analyzes its asymptotic behavior in stochastic processes.

Contribution

It introduces a novel perspective by linking binary search tree paths to real-valued functions and investigates their asymptotic properties.

Findings

Characterization of the silhouette as a stochastic process

Asymptotic behavior of the silhouette for binary search trees

Insights into the structure of binary search trees through the silhouette

Abstract

A zero-one sequence describes a path through a rooted directed binary tree $T$; it also encodes a real number in $[0,1]$. We regard the level of the external node of $T$ along the path as a function on the unit interval, the silhouette of $T$. We investigate the asymptotic behavior of the resulting stochastic processes for sequences of trees that are generated by the binary search tree algorithm.