The shortest path problem is a class of typical problems in graph theory and network science, it has a wide range of application scenarios. At present, the parallel single-source shortest path algorithm is mainly used to solve the all-pair shortest path problems. We propose a novel all-pair shortest path algorithm based on block matrix multiplication via GPUs. Our key advancement is transforming the shortest path problems into the linear algebra problems, taking advantage of the GPUs' performance ascendancy in this regard. In the experiments, the novel algorithm achieves average of 41.257$\times$ and the maximum of 89.919$\times$ over Dijkstra algorithm which implements the priority queue by the binary heap and optimized via multi-threaded.

翻译：最短路径问题是图表理论和网络科学的典型问题,它有各种各样的应用情景。目前,平行的单一来源最短路径算法主要用于解决所有最短路径问题。我们建议采用新的全帕最短路径算法,其基础是块式矩阵乘以GPUs的乘法。我们的关键进步是利用GPUs在这方面的性能提升,将最短路径问题转化为线性代数问题。在实验中,新式算法平均达到41.257美元,最多达到89.919美元,超过Dijkstra算法,该算法通过二进制堆进行优先排队,并通过多读进行优化。