Review of Three Algorithms That Build k-d Trees

TL;DR

This paper reviews three algorithms for constructing balanced k-d trees, analyzing their partitioning techniques, computational complexities, and introduces a dual-threaded approach for one algorithm to improve performance.

Contribution

It compares three different k-d tree-building algorithms and proposes a dual-threaded implementation for enhanced efficiency.

Findings

Partitioning technique impacts construction complexity

Performance varies among the three algorithms

Dual-threaded execution improves build speed

Abstract

The original description of the k-d tree recognized that rebalancing techniques, such as used to build an AVL tree or a red-black tree, are not applicable to a k-d tree. Hence, in order to build a balanced k-d tree, it is necessary to find the median of a set of data for each recursive subdivision of that set. The sort or selection used to find the median, and the technique used to partition the set about that median, strongly influence the computational complexity of building a k-d tree. This article describes and contrasts three k-d tree-building algorithms that differ in their technique used to partition the set, and compares the performance of the algorithms. In addition, dual-threaded execution is proposed for one of the three algorithms.