Efficient top-down updates in AVL trees

TL;DR

This paper introduces an algorithm for AVL trees that performs top-down rebalancing with a fixed look-ahead, achieving efficient updates with an amortised constant number of write operations, addressing longstanding open questions.

Contribution

It presents the first algorithm that performs top-down rebalancing in AVL trees with constant amortised write operations per update.

Findings

Successfully performs top-down rebalancing in AVL trees.

Achieves amortised constant write operations per update.

Addresses two major open questions in AVL tree rebalancing.

Abstract

Since AVL trees were invented in 1962, two major open questions about rebalancing operations, which found positive answers in other balanced binary search trees, were left open: can these operations be performed top-down (with a fixed look-ahead), and can they use an amortised constant number of write operations per update? We propose an algorithm that answers both questions positively.