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

Abstract

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.