This paper presents a blocked united algorithm for the all-pairs 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.

The All-Pairs Shortest Paths (APSP) problem is a graph problem which can be solved by a three-nested loop program. The Cell Broadband Engine (Cell/B.E.) is a heterogeneous multi-core processor that offers the high single precision floating-point performance. In this paper, a solution of the APSP problem on the Cell/B.E. is presented. To maximize the performance of the Cell/B.E., a blocked algorithm for the APSP problem is used. The blocked algorithm enables reuse of data in registers and utilizes the memory hierarchy. We also describe several optimization techniques for effective implementation of the APSP problem on the Cell/B.E. The Cell/B.E. achieves the performance of 8.45 Gflop/s for the APSP problem by using one SPE and 50.6 Gflop/s by using six SPEs.