All-Pairs Shortest Path algorithms for planar graph for GPU-accelerated clusters

• We develop a new approach for the All-Pairs Shortest Path problem in planar graphs.
• We target execution on large CPU–GPU clusters and graphs with millions of vertices.
• We design a centralized (master/slave) and a decentralized (distributed) version.
• Our algorithms are work-efficient and allow a high-degree of parallelism.
• Our algorithms are significantly faster than the previous ones.

We present a new approach for solving the All-Pairs Shortest-Path (APSP) problem for planar graphs that exploits the massive on-chip parallelism available in today’s Graphics Processing Units (GPUs). We describe two new algorithms based on our approach. Both algorithms use Floyd–Warshall method, have near optimal complexity in terms of the total number of operations, while their 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 fastest known Dijkstra-based GPU implementation and a two-fold speedup over a parallel Dijkstra-based CPU implementation.