Exploring the Design Space of Static and Incremental Graph Connectivity Algorithms on GPUs

TL;DR

This paper explores various design choices for GPU-based static and incremental graph connectivity algorithms, introducing over 300 implementations that significantly outperform existing methods in speed and throughput.

Contribution

It systematically investigates design options like sampling, linking, and tree compression, creating numerous GPU algorithms with improved performance for connectivity tasks.

Findings

Achieves 2.47x speedup over existing static algorithms.

Reaches up to 48.23 billion edges/sec in incremental setting.

Outperforms CPU implementations by up to 14.51x.

Abstract

Connected components and spanning forest are fundamental graph algorithms due to their use in many important applications, such as graph clustering and image segmentation. GPUs are an ideal platform for graph algorithms due to their high peak performance and memory bandwidth. While there exist several GPU connectivity algorithms in the literature, many design choices have not yet been explored. In this paper, we explore various design choices in GPU connectivity algorithms, including sampling, linking, and tree compression, for both the static as well as the incremental setting. Our various design choices lead to over 300 new GPU implementations of connectivity, many of which outperform state-of-the-art. We present an experimental evaluation, and show that we achieve an average speedup of 2.47x speedup over existing static algorithms. In the incremental setting, we achieve a throughput of up to 48.23 billion edges per second. Compared to state-of-the-art CPU implementations on a 72-core machine, we achieve a speedup of 8.26--14.51x for static connectivity and 1.85--13.36x for incremental connectivity using a Tesla V100 GPU.