A Sparsity-Aware Distributed-Memory Algorithm for Sparse-Sparse Matrix Multiplication

Multiplying two sparse matrices (SpGEMM) is a common computational primitive used in many areas including graph algorithms, bioinformatics, algebraic multigrid solvers, and randomized sketching. Distributed-memory parallel algorithms for SpGEMM have mainly focused on sparsity-oblivious approaches th...

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Bibliographic Details
Published in:SC24: International Conference for High Performance Computing, Networking, Storage and Analysis pp. 1 - 14
Main Authors: Hong, Yuxi, Buluc, Aydin
Format: Conference Proceeding
Language:English
Published: IEEE 17.11.2024
Subjects:
1D algorithm
1D SpGEMM algorithm
Electric breakdown
High performance computing
Load management
Matrices
numerical linear algebra
Parallel algorithms
parallel computing
Partitioning algorithms
RDMA
Software
Software algorithms
Sparse matrices
sparse matrix-matrix multiplication
sparsity-aware 1D SpGEMM algorithm
SpGEMM
Three-dimensional displays
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Summary:Multiplying two sparse matrices (SpGEMM) is a common computational primitive used in many areas including graph algorithms, bioinformatics, algebraic multigrid solvers, and randomized sketching. Distributed-memory parallel algorithms for SpGEMM have mainly focused on sparsity-oblivious approaches that use 2D and 3D partitioning. Sparsity-aware 1D algorithms can theoretically reduce communication by not fetching nonzeros of the sparse matrices that do not participate in the multiplication. Here, we present a distributed-memory 1D SpGEMM algorithm and implementation. It uses MPI RDMA operations to mitigate the cost of packing/unpacking submatrices for communication, and it uses a block fetching strategy to avoid excessive finegrained messaging. Our results show that our 1D implementation outperforms state-of-the-art 2D and 3D implementations within CombBLAS for many configurations, inputs, and use cases, while remaining conceptually simpler.
DOI:10.1109/SC41406.2024.00053