GPU-friendly, Parallel, and (Almost-)In-Place Construction of Left-Balanced k-d Trees

TL;DR

This paper introduces a GPU-friendly, parallel algorithm for constructing left-balanced k-d trees efficiently, requiring minimal temporary storage and leveraging parallel sorting and CUDA kernels.

Contribution

The paper presents a novel parallel and GPU-optimized algorithm for building left-balanced k-d trees with minimal memory overhead and simple iterative steps.

Findings

Efficient construction of k-d trees on GPU with minimal temporary storage.

Algorithm requires only one integer per data point and O(log N) iterations.

Achieves parallelism through sorting and CUDA kernels.

Abstract

We present an algorithm that allows for building left-balanced and complete k-d trees over k-dimensional points in a trivially parallel and GPU friendly way. Our algorithm requires exactly one int per data point as temporary storage, and uses O(log N) iterations, each of which performs one parallel sort, and one trivially parallel CUDA per-node update kernel.