A work-efficient parallel sparse matrix-sparse vector multiplication algorithm

TL;DR

This paper presents a work-efficient multithreaded algorithm for sparse matrix-sparse vector multiplication that improves performance and scalability across diverse graph-related matrices on modern manycore processors.

Contribution

The paper introduces a simple, work-efficient parallel SpMSpV algorithm that avoids per-thread matrix scans and performs well on various sparse matrices, enhancing existing methods.

Findings

Achieves up to 15x speedup on 24-core processors

Attains up to 49x speedup on 64-core manycore processors

Performs efficiently on diverse matrices with heterogeneous sparsity patterns

Abstract

We design and develop a work-efficient multithreaded algorithm for sparse matrix-sparse vector multiplication (SpMSpV) where the matrix, the input vector, and the output vector are all sparse. SpMSpV is an important primitive in the emerging GraphBLAS standard and is the workhorse of many graph algorithms including breadth-first search, bipartite graph matching, and maximal independent set. As thread counts increase, existing multithreaded SpMSpV algorithms can spend more time accessing the sparse matrix data structure than doing arithmetic. Our shared-memory parallel SpMSpV algorithm is work efficient in the sense its total work is proportional to the number of arithmetic operations required. The key insight is to avoid each thread individually scan the list of matrix columns. Our algorithm is simple to implement and operates on existing column-based sparse matrix formats. It performs well on diverse matrices and vectors with heterogeneous sparsity patterns. A high-performance implementation of the algorithm attains up to 15x speedup on a 24-core Intel Ivy Bridge processor and up to 49x speedup on a 64-core Intel KNL manycore processor. In contrast to implementations of existing algorithms, the performance of our algorithm is sustained on a variety of different input types include matrices representing scale-free and high-diameter graphs.