Probabilistic AVL Trees (p-AVL): Relaxing Deterministic Balancing

TL;DR

This paper empirically investigates the behavior of p-AVL trees, a probabilistic variant of AVL trees, showing that even small probabilities significantly alter their structure.

Contribution

It provides a detailed empirical analysis of p-AVL trees, highlighting how probabilistic balancing impacts their structure compared to deterministic AVL trees.

Findings

Small nonzero p causes significant structural changes.

p-AVL trees interpolate between BST and AVL trees.

Empirical patterns of rotations and imbalance events are documented.

Abstract

This paper studies the empirical behaviour of the p-AVL tree, a probabilistic variant of the AVL tree in which each imbalance is repaired with probability $p$. This gives an exact continuous interpolation from $p = 0$, which recovers the BST endpoint, to $p = 1$, which recovers the standard AVL tree. Across random-order insertion experiments, we track rotations per node, total imbalance events, average depth, average height, and a global imbalance statistic $\sigma$. The main empirical result is that even small nonzero p already causes a strong structural change. The goal here is empirical rather than fully theoretical: to document the behaviour of the p-AVL family clearly and identify the main patterns.