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.

翻译：根生成树（RST）是并行图分析中的核心原语，是双连通分量和平面性测试等算法的基础。在GPU上，RST构建传统上依赖于广度优先搜索（BFS），因其简单性和工作高效性。然而，BFS具有O(D)的步长复杂度，这在面对高直径和幂律图时严重限制了并行性。本文对现代GPU上的替代RST构建策略进行了比较研究。我们提出了路径反转RST（PR-RST）算法的GPU适配版本，针对现代GPU架构优化了其指针跳转和广播操作。此外，我们评估了一种集成方法，该方法将最先进的连通性框架（GConn）与基于欧拉环游的根生成技术相结合。在超过10个真实世界图上的实验结果表明，基于GConn的方法在高直径图上相比优化的BFS实现了高达300倍的加速。这些发现表明，基于连通性方法的O(log n)步长复杂度在现代硬件上可以抵消其结构开销，这促使我们重新思考GPU图分析中的RST构建策略。