Implementation of a Parallel Tree Method on a GPU

TL;DR

This paper presents a GPU-based parallel implementation of the kd-tree algorithm, significantly improving the efficiency of particle interaction computations by leveraging cache optimization and detailed performance testing.

Contribution

The paper introduces a novel parallel GPU implementation of the kd-tree method with specific optimizations like localized particle ordering for enhanced cache utilization.

Findings

GPU implementation achieves practical and efficient tree traversal.

Performance measurements demonstrate significant speedup over CPU methods.

Localized particle ordering improves cache efficiency and overall performance.

Abstract

The kd-tree is a fundamental tool in computer science. Among other applications, the application of kd-tree search (by the tree method) to the fast evaluation of particle interactions and neighbor search is highly important, since the computational complexity of these problems is reduced from O(N^2) for a brute force method to O(N log N) for the tree method, where N is the number of particles. In this paper, we present a parallel implementation of the tree method running on a graphics processing unit (GPU). We present a detailed description of how we have implemented the tree method on a Cypress GPU. An optimization that we found important is localized particle ordering to effectively utilize cache memory. We present a number of test results and performance measurements. Our results show that the execution of the tree traversal in a force calculation on a GPU is practical and efficient.