Parallel sparse matrix-matrix multiplication algorithms (PSpGEMM) spend most of their running time on inter-process communication. In the case of distributed matrix-matrix multiplications, much of this time is spent on interchanging the partial results that are needed to calculate the final product matrix. This overhead can be reduced with a one-dimensional distributed algorithm for parallel sparse matrix-matrix multiplication that uses a novel accumulation pattern based on the logarithmic complexity of the number of processors (i.e., O (log (p)) where p is the number of processors). This algorithm's MPI communication overhead and execution time were evaluated on an HPC cluster, using randomly generated sparse matrices with dimensions up to one million by one million. The results showed a reduction of inter-process communication overhead for matrices with larger dimensions compared to another one dimensional parallel algorithm that takes O(p) run-time complexity for accumulating the results.

<p dir="ltr">Heterogeneous clusters with nodes containing one or more accelerators, such as GPUs, have become common. While MPI provides inter-address space communication, and OpenCL provides a process with access to heterogeneous computational resources, programmers are forced to write hybrid programs that manage the interaction of both of these systems. This paper describes an array programming interface that provides users with automatic and manual distributions of data and work. Using work distribution and kernel def and use information, communication among processes and devices in a process is performed automatically. By providing a unified programming model to the user, program development is simplified.</p>