An Efficient GPU General Sparse Matrix-Matrix Multiplication for Irregular Data

Abstract—General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method, breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM algorithm has to handle extra irregularity from three aspects: (1) the number of the nonzero entries in the result sparse matrix is unknown in advance, (2) very expensive parallel insert operations at random positions in the result sparse matrix dominate the execution time, and (3) load balancing must account for sparse data in both input matrices. Recent work on GPU SpGEMM has demonstrated rather good both time and space complexity, but works best for fairly regular matrices. In this work we present a GPU SpGEMM algorithm that particularly focuses on the above three problems. Memory pre-allocation for the result matrix is organized by a hybrid method that saves a large amount of global memory space and efficiently utilizes the very limited on-chip scratchpad memory. Parallel insert operations of the nonzero entries are implemented through the GPU merge path algorithm that is experimentally found to be the fastest GPU merge approach. Load balancing builds on the number of the necessary arith-metic operations on the nonzero entries and is guaranteed in all stages. Compared with the state-of-the-art GPU SpGEMM methods in the CUSPARSE library and the CUSP library and the latest CPU SpGEMM method in the Intel Math Kernel Library, our approach delivers excellent absolute performance and relative speedups on a benchmark suite composed of 23 matrices with diverse sparsity structures. Keywords-sparse matrices; matrix multiplication; linear al-gebra; GPU; merging; parallel algorithms; I