Beyond BFS: A Comparative Study of Rooted Spanning Tree Algorithms on GPUs

TL;DR

This paper compares rooted spanning tree algorithms on GPUs, introducing a new GPU-optimized Path Reversal RST method and demonstrating that connectivity-based approaches can significantly outperform BFS on high-diameter graphs.

Contribution

It presents a GPU-adapted Path Reversal RST algorithm and evaluates a combined connectivity and Eulerian tour approach, challenging BFS dominance in GPU graph analytics.

Findings

GConn-based approach achieves up to 300x speedup over BFS on high-diameter graphs.

Connectivity methods with O(log n) steps can outperform traditional BFS on modern GPUs.

The study encourages rethinking RST construction strategies for GPU-based graph analytics.

Abstract

Rooted spanning trees (RSTs) are a core primitive in parallel graph analytics, underpinning algorithms such as biconnected components and planarity testing. On GPUs, RST construction has traditionally relied on breadth-first search (BFS) due to its simplicity and work efficiency. However, BFS incurs an O(D) step complexity, which severely limits parallelism on high-diameter and power-law graphs. We present a comparative study of alternative RST construction strategies on modern GPUs. We introduce a GPU adaptation of the Path Reversal RST (PR-RST) algorithm, optimizing its pointer-jumping and broadcast operations for modern GPU architecture. In addition, we evaluate an integrated approach that combines a state-of-the-art connectivity framework (GConn) with Eulerian tour-based rooting. Across more than 10 real-world graphs, our results show that the GConn-based approach achieves up to 300x speedup over optimized BFS on high-diameter graphs. These findings indicate that the O(log n) step complexity of connectivity-based methods can outweigh their structural overhead on modern hardware, motivating a rethinking of RST construction in GPU graph analytics.