Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

TL;DR

This paper presents the first practical implementation of a 3D parallel algorithm for sparse matrix-matrix multiplication, significantly improving performance by exploiting multiple levels of parallelism and analyzing bottlenecks.

Contribution

It introduces the first practical implementation of 3D SpGEMM that leverages multi-level parallelism, demonstrating substantial speedups over existing codes.

Findings

Achieves significant speedups over state-of-the-art codes

Identifies bottlenecks for further optimization

Validates the effectiveness of 3D parallelism in SpGEMM

Abstract

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdos-Renyi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first ever implementation of the 3D SpGEMM formulation that also exploits multiple (intra-node and inter-node) levels of parallelism, achieving significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research.