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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| Published in: | SC24: International Conference for High Performance Computing, Networking, Storage and Analysis pp. 1 - 14 |
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IEEE
17.11.2024
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Buluc, Aydin Hong, Yuxi |
| Author_xml | – sequence: 1 givenname: Yuxi surname: Hong fullname: Hong, Yuxi email: abuluc@lbl.gov organization: Applied Math & Computational Research Division Lawrence Berkeley National Laboratory,Berkeley,USA – sequence: 2 givenname: Aydin surname: Buluc fullname: Buluc, Aydin organization: Applied Math & Computational Research Division Lawrence Berkeley National Laboratory,Berkeley,USA |
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| Snippet | Multiplying two sparse matrices (SpGEMM) is a common computational primitive used in many areas including graph algorithms, bioinformatics, algebraic multigrid... |
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| SubjectTerms | 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 |
| Title | A Sparsity-Aware Distributed-Memory Algorithm for Sparse-Sparse Matrix Multiplication |
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