Blocked United Algorithm for the All-Pairs Shortest Paths Problem on Hybrid CPU-GPU Systems

This paper presents a blocked united algorithm for the allpairs shortest paths (APSP) problem. This algorithm simultaneously computes both the shortest-path distance matrix and the shortest-path construction matrix for a graph. It is designed for a high-speed APSP solution on hybrid CPU-GPU systems. In our implementation, two most compute intensive parts of the algorithm are performed on the GPU. The first part is to solve the APSP sub-problem for a block of sub-matrices, and the other part is a matrix-matrix “multiplication” for the APSP problem. Moreover, the amount of data communication between CPU (host) memory and GPU memory is reduced by reusing blocks once sent to the GPU. When a problem size (the number of vertices in a graph) is large enough compared to a block size, our implementation of the blocked algorithm requires CPU GPU exchanging of three blocks during a block computation on the GPU. We measured the performance of the algorithm implementation on two different CPU-GPU systems. A system containing an Intel Sandy Bridge CPU (Core i7 2600K) and an AMD Cayman GPU (Radeon HD 6970) achieves the performance up to 1.1 TFlop/s in a single precision. key words: all-pairs shortest paths problem, path construction, FloydWarshall algorithm, blocked algorithm, hybrid CPU-GPU systems