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We consider a sparse matrix-matrix multiplication (SpGEMM) setting where one matrix is square and the other is tall and skinny. This special variant, TS-SpGEMM, has important applications in multi-source breadth-first search, influence maximization, sparse graph embedding, and algebraic multigrid solvers. Unfortunately, popular distributed algorithms like sparse SUMMA deliver suboptimal performance for TS-SpGEMM. To address this limitation, we develop a novel distributed-memory algorithm tailored for TS SpGEMM. Our approach employs customized 1D partitioning for all matrices involved and leverages sparsity-aware tiling for efficient data transfers. In addition, it minimizes communication overhead by incorporating both local and remote computations. On average, our TSSpGEMM algorithm attains 5x performance gains over 2D and 3D SUMMA. Furthermore, we use our algorithm to implement multi-source breadth-first search and sparse graph embedding algorithms and demonstrate their scalability up to 512 Nodes (or 65,536 cores) on NERSC Perlmutter. 

Sparse matrix dense matrix multiplication (SpMM) is commonly used in applications ranging from scientific computing to graph neural networks. Typically, when SpMM is executed in a distributed platform, communication costs dominate. Such costs depend on how communication is scheduled. If it is scheduled in a sparsity-unaware manner, such as with collectives, execution is often inefficient due to unnecessary data transfers. On the other hand, if communication is scheduled in a fine-grained sparsity-aware manner, communicating only the necessary data, execution can also be inefficient due to high software overhead. We observe that individual sparse matrices often contain regions that are denser and regions that are sparser. Based on this observation, we develop a model that partitions communication into sparsity-unaware and sparsity-aware components. Leveraging the partition, we develop a new algorithm that performs collective communication for the denser regions, and fine-grained, one-sided communication for the sparser regions. We call the algorithm Two-Face. We show that Two-Face attains an average speedup of 2.11x over prior work when evaluated on a 4096-core supercomputer. Additionally, Two-Face scales well with the machine size. 

Sparse Matrix-Vector Multiplication (SpMV) is an essential sparse kernel. Numerous methods have been developed to accelerate SpMV. However, no single method consistently gives the highest performance across a wide range of matrices. For this reason, a performance prediction model is needed to predict the best SpMV method for a given sparse matrix. Unfortunately, predicting SpMV’s performance is challenging due to the diversity of factors that impact it. In this work, we develop a machine learning framework called WISE that accurately predicts the magnitude of the speedups of different SpMV methods over a baseline method for a given sparse matrix. WISE relies on a novel feature set that summarizes a matrix’s size, skew, and locality traits. WISE can then select the best SpMV method for each specific matrix. With a set of nearly 1,500 matrices, we show that using WISE delivers an average speedup of 2.4× over using Intel’s MKL in a 24-core server.