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A task parallel algorithm for finding all-pairs shortest paths using the GPU

This paper proposes an acceleration method for finding the all-pairs shortest paths (APSPs) using the graphics processing unit (GPU). Our method is based on Harish's iterative algorithm that computes the cost of the single-source shortest path (SSSP) in parallel on the GPU. In addition to this fine-grained parallelism, we exploit the coarse-grained parallelism by using a task parallelisation scheme that associates a task with an SSSP problem. This scheme solves multiple SSSP problems at a time, allowing us to efficiently access graph data by sharing the data between processing elements in the GPU. Furthermore, our fine-and coarse-grained parallelisation leads to a higher parallelism, increasing the efficiency with highly threaded code. As a result, the speedup over the previous SSSP-based implementation ranges from a factor of 2.8 to that of 13, depending on the graph topology. We also show that the overhead of path recording needed after cost computation increases the execution time by 7.7%.