A Dynamic, Self-balancing k-d Tree

Russell A. Brown

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arXiv · 2509.08148

A Dynamic, Self-balancing k-d Tree

Russell A. Brown

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Abstract

The original description of the k-d tree recognized that rebalancing techniques, used for building an AVL or red-black tree, are not applicable to a k-d tree, because these techniques involve cyclic exchange of tree nodes that violates the invariant of the k-d tree. For this reason, a static, balanced k-d tree is often built from all of the k-dimensional data en masse. However, it is possible to build a dynamic k-d tree that self-balances when necessary after insertion or deletion of each k-dimensional datum. This article describes insertion, deletion, and rebalancing algorithms for a dynamic, self-balancing k-d tree, and measures their performance.

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Russell A. Brown. 2025-09-09. A Dynamic, Self-balancing k-d Tree. https://arxiv.org/abs/2509.08148

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