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arXiv · 2112.10223

Parallel Algorithms for Adding a Collection of Sparse Matrices

Md Taufique Hussain·Guttu Sai Abhishek·Aydin Buluç·Ariful Azad
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Abstract

We develop a family of parallel algorithms for the SpKAdd operation that adds a collection of k sparse matrices. SpKAdd is a much needed operation in many applications including distributed memory sparse matrix-matrix multiplication (SpGEMM), streaming accumulations of graphs, and algorithmic sparsification of the gradient updates in deep learning. While adding two sparse matrices is a common operation in Matlab, Python, Intel MKL, and various GraphBLAS libraries, these implementations do not perform well when adding a large collection of sparse matrices. We develop a series of algorithms using tree merging, heap, sparse accumulator, hash table, and sliding hash table data structures. Among them, hash-based algorithms attain the theoretical lower bounds both on the computational and I/O complexities and perform the best in practice. The newly-developed hash SpKAdd makes the computation of a distributed-memory SpGEMM algorithm at least 2x faster than that the previous state-of-the-art algorithms.

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Md Taufique Hussain, Guttu Sai Abhishek, Aydin Buluç, Ariful Azad. 2021-12-19. Parallel Algorithms for Adding a Collection of Sparse Matrices. https://arxiv.org/abs/2112.10223

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