We describe a new algorithm for solving the all-pairs shortest-path (APSP) problem for planar graphs and graphs with small separators that exploits the massive on-chip parallelism available in today’s Graphics Processing Units (GPUs). Our algorithm, based on the Floyd-Warshall algorithm, has near optimal complexity in terms of the total number of operations, while its matrix-based structure is regular enough to allow for efficient parallel implementation on the GPUs. By applying a divide-and-conquer approach, we are able to make use of multi-node GPU clusters, resulting in more than an order of magnitude speedup over the fastest known Dijkstra-based GPU implementation and a two-fold speedup over a parallel Dijkstra-based CPU implementation.
(Hristo Djidjev, Sunil Thulasidasan, Guillaume Chapuis, Rumen Andonov and Dominique Lavenier: “Efficient Multi-GPU Computation of All-Pairs Shortest Paths”. To appear in IEEE International Parallel and Distributed Processing Symposium (IPDPS), May 2014. [PDF])