大型稀疏图中的快速全对最短路径算法

Shaofeng Yang, Xiandong Liu, Yun-Tsz Wang, Xin He, Guangming Tan
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引用次数: 3

摘要

在图中寻找全对最短路径(APSP)是求解各种域的关键。由于实际应用中图的稀疏性,我们将整个图以压缩存储格式存储在分布式计算集群的每个进程中,并将Floyd算法与Dijkstra算法相结合来解决APSP问题,从而产生了新的快速APSP算法。与最先进的Part APSP算法相比,我们的算法增加了一些内存开销来存储原始稀疏图,并同时使用局部Floyd和全局Dijkstra算法。这样做的好处是避免了昂贵的全局通信,减少了一个本地FW操作,简化了Minplus功能,并使其数据访问连续。此外,我们提出了一个并行框架来解决图形处理器数量与图的可分块数量不匹配的问题。与CPU Dijkstra算法相比,Fast APSP算法的平均加速速度为16.97倍,与GPU Dijkstra算法相比为7.09倍,与Part APSP算法相比为7.09倍,与去中心化Part APSP算法相比为4.6倍。在实验中也显示出良好的可扩展性。对于有11548845个顶点的图形,使用2048个gpu来解决APSP问题大约需要12.45分钟。
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Fast All-Pairs Shortest Paths Algorithm in Large Sparse Graph
Finding the All-Pairs Shortest Paths (APSP) in a graph is the key for various domains. Motivated by the graphs are sparse in most real-world applications, we store the whole graph as a compressed storage format in each process of the distributed computing clusters and combine the Floyd algorithm with the Dijkstra algorithm to solve the APSP problem in this work, which leads to the novel Fast APSP algorithm. In contrast to the state-of-the-art Part APSP algorithm, our algorithm adds some memory overhead to store the original sparse graph and uses local Floyd and global Dijkstra algorithms simultaneously. The payoff is the circumvention of expensive global communication, reducing one local FW operation, simplifying the Minplus function, and making its data access continuous. Furthermore, we propose a parallel framework to solve the problem of mismatch between the number of GPUs and the number of divisible blocks of a graph. The Fast APSP algorithm exhibits an average speedup of 16.97x compared to the CPU Dijkstra algorithm, 7.09x compared to the GPU Dijkstra algorithm, 7.09x compared to the Part APSP algorithm, and 4.6x compared to the decentralized Part APSP algorithm. It also shows good scalability in our experiments. It takes about 12.45 minutes to solve the APSP problem for the graph with 11,548,845 vertices by engaging 2048 GPUs.
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