Highly Parallel Sparse Matrix-Matrix Multiplication

Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on two-dimensional block distribution of sparse matrices where serial sections use a novel hypersparse kernel for scalability. We give a state-of-the-art MPI implementation of one of our algorithms. Our experiments show scaling up to thousands of processors on a variety of test scenarios.