🤖 AI Summary
This work addresses the limitations of traditional BFS-based rooted spanning tree (RST) construction, which suffers from O(D) step complexity and poor parallel scalability on high-diameter and power-law graphs. The authors present the first GPU-optimized implementation of the Path Reversal RST (PR-RST) algorithm, integrating the GConn connectivity framework with Euler tour-based rooting, and introducing GPU-tailored optimizations including pointer jumping and broadcast enhancements. Experimental evaluation across more than ten real-world graph datasets demonstrates that the proposed method achieves up to 300× speedup over highly optimized BFS baselines, with particularly pronounced gains on high-diameter graphs. These results substantiate the efficiency and scalability of O(log n) step-complexity connectivity strategies in modern parallel architectures.
📝 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.