GPU-accelerated shortest paths computations for planar graphs

We describe three algorithms and their associated graphics processing unit (GPU) implementations for two types of shortest path problems. These implementations target computations on graphs with up to millions of vertices and executions on GPU clusters. The first two algorithms solve the All-Pairs Shortest Path problem. The first of these two algorithms allows computations on graphs with negative edges, while the second trades this ability for better parallel scaling properties and improved memory access. The third algorithm solves the Single-Pair Shortest Path query problem. Our implementations efficiently exploit the computational power of 256 GPUs simultaneously. All shortest paths of a million vertex graphs can be computed in 6 min and shortest path queries on the same graph are answered in a quarter of a millisecond. These implementations proved to be orders of magnitude faster than existing parallel approaches.