Sparse matrix-sparse vector multiplication (SpMSpV) is an important primitive for graph algorithms and machine learning applications. The sparsity of the input and output vectors makes its floating point efficiency in general lower than sparse matrix-vector multiplication (SpMV) and sparse matrix-matrix multiplication (SpGEMM). Existing parallel SpMSpV methods focused on various row- and column-wise storage formats and merging operations. However, the data locality and sparsity pattern of the input matrix and vector are largely ignored.

Sparse general matrix-matrix multiplication (SpGEMM) is one of the most fundamental building blocks in sparse linear solvers, graph processing frameworks and machine learning applications. The existing parallel approaches for shared memory SpGEMM mostly use the row-row style with possibly good parallelism. However, because of the irregularity in sparsity structures, the existing row-row methods often suffer from three problems: (1) load imbalance, (2) high global space complexity and unsatisfactory data locality, and (3) sparse accumulator selection.