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This paper compares different rooted spanning tree (RST) construction algorithms on GPUs, moving beyond the traditional reliance on breadth-first search (BFS). They introduce a GPU-optimized Path Reversal RST (PR-RST) algorithm and evaluate an integrated approach combining a connectivity framework (GConn) with Eulerian tour-based rooting. Results on real-world graphs demonstrate that the GConn-based approach achieves up to 300x speedup over optimized BFS on high-diameter graphs, highlighting the benefits of connectivity-based methods for RST construction on GPUs.
Connectivity-based methods for rooted spanning tree construction on GPUs can achieve up to 300x speedup over BFS on high-diameter graphs, challenging the dominance of BFS in this domain.
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.
