A single-tree algorithm to compute the Euclidean minimum spanning tree on GPUs

TL;DR

This paper introduces a GPU-optimized Borůvka-based algorithm for efficiently computing Euclidean minimum spanning trees, achieving significant speedups over CPU methods and demonstrating high scalability and portability across diverse hardware.

Contribution

The paper presents a novel single-tree Borůvka-based GPU algorithm for EMST that reduces distance calculations and improves performance and portability.

Findings

Achieves 4-24x speedup over CPU implementations.

Successfully computes EMST for 37 million 3D points in under 0.5 seconds on a single GPU.

Demonstrates scalability and hardware portability across multiple GPU architectures.

Abstract

Computing the Euclidean minimum spanning tree (EMST) is a computationally demanding step of many algorithms. While work-efficient serial and multithreaded algorithms for computing EMST are known, designing an efficient GPU algorithm is challenging due to a complex branching structure, data dependencies, and load imbalances. In this paper, we propose a single-tree Bor\r{u}vka-based algorithm for computing EMST on GPUs. We use an efficient nearest neighbor algorithm and reduce the number of the required distance calculations by avoiding traversing subtrees with leaf nodes in the same component. The developed algorithms are implemented in a performance portable way using ArborX, an open-source geometric search library based on the Kokkos framework. We evaluate the proposed algorithm on various 2D and 3D datasets, show and compare it with the current state-of-the-art open-source CPU implementations. We demonstrate 4-24x speedup over the fastest multi-threaded implementation. We prove the portability of our implementation by providing results on a variety of hardware: AMD EPYC 7763, Nvidia A100 and AMD MI250X. We show scalability of the implementation, computing EMST for 37 million 3D cosmological dataset in under a 0.5 second on a single A100 Nvidia GPU.