Parallel Algorithms for Masked Sparse Matrix-Matrix Products

TL;DR

This paper introduces novel parallel algorithms and data structures for efficient Masked SpGEMM, significantly outperforming existing methods by considering mask structures and cache behavior on shared-memory systems.

Contribution

It presents new algorithms and guidelines for fast Masked SpGEMM that incorporate mask considerations directly into the computation process.

Findings

Algorithms outperform state-of-the-art in most cases

Performance depends on matrix and mask density and structure

Cache behavior significantly impacts efficiency

Abstract

Computing the product of two sparse matrices (SpGEMM) is a fundamental operation in various combinatorial and graph algorithms as well as various bioinformatics and data analytics applications for computing inner-product similarities. For an important class of algorithms, only a subset of the output entries are needed, and the resulting operation is known as Masked SpGEMM since a subset of the output entries is considered to be "masked out". Existing algorithms for Masked SpGEMM usually do not consider mask as part of multiplication and either first compute a regular SpGEMM followed by masking, or perform a sparse inner product only for output elements that are not masked out. In this work, we investigate various novel algorithms and data structures for this rather challenging and important computation, and provide guidelines on how to design a fast Masked-SpGEMM for shared-memory architectures. Our evaluations show that factors such as matrix and mask density, mask structure and cache behavior play a vital role in attaining high performance for Masked SpGEMM. We evaluate our algorithms on a large number of matrices using several real-world benchmarks and show that our algorithms in most cases significantly outperform the state of the art for Masked SpGEMM implementations.