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arXiv · 2604.02223

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

Hayagriv Desikan
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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.

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Hayagriv Desikan. 2026-04-02. Probabilistic AVL Trees (p-AVL): Relaxing Deterministic Balancing. https://arxiv.org/abs/2604.02223

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