TileSpMSpV: A Tiled Algorithm for Sparse Matrix-Sparse Vector Multiplication on GPUs.

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. We in this paper propose TileSpMSpV, a tiled algorithm for accelerating SpMSpV on GPUs. Firstly, tile-wise storage structures are developed for fast positioning a group of nonzeros in matrix and vectors. Then, we develop the TileSpMSpV algorithm on top of the storage structures. In addition, to accelerate directional optimization breadth-first search (BFS) by using TileSpMSpV, we propose a TileBFS algorithm including three kernels called Push-CSC, Push-CSR and Pull-CSC. In the experiments running on a high-end NVIDIA GPU and using 2757 sparse matrices, the TileSpMSpV algorithm outperforms TileSpMV, cuSPARSE and CombBLAS by a factor of on average 1.83, 17.18 and 17.20 (up to 7.68, 1050.02 and 235.90), respectively. Moreover, our TileBFS algorithm outperforms Gunrock and GSwitch by a factor of on average 2.88 and 4.52 (up to 21.35 and 1000.85), respectively.