Highly Parallel Sparse Matrix-Matrix Multiplication

TL;DR

This paper introduces highly parallel algorithms for sparse matrix-matrix multiplication, enabling scalable performance on thousands of processors, which benefits high-performance graph algorithms and linear solvers.

Contribution

It presents the first parallel algorithms with increasing speedups for unbounded processors, utilizing a novel hypersparse kernel and 2D block distribution.

Findings

Achieves scalable performance up to thousands of processors

Demonstrates effectiveness on diverse test scenarios

Provides a state-of-the-art MPI implementation

Abstract

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.