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 arithmetic 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.

GPU-Accelerated Sparse Matrix-Matrix Multiplication by Iterative Row Merging

“…The performance rate is defined as the ratio of the arithmetic workload and the measured processing time. The arithmetic workload flops(A,B) is defined as twice the number of nontrivial scalar multiplications (to account for the additions) which can be computed as j∈âi: nnz(b j: ) for each result row c i: [12,31], whereâ i: denotes the nonzero indices of row a i: . All performance rate measurements were repeated 11 times and the median was used because of its robustness with respect to outliers.…”

“…Table 1, were taken from the University of Florida Sparse Matrix Collection [13]. Inspired by [31], we sorted the matrices into regular (the upper 10) and irregular matrices (the lower 11) and sorted these subsets alphabetically. Regular matrices result from problems involving mesh approximations, e.g., from finite element methods, while irregular matrices mostly result from network structures.…”

Accelerating the Detection of Spectral Bands by ANN-ED on a GPU

“…Parallelization of the computation on the Device is done mainly in the matrix product (Liu & Vinter, 2014) and in the calculation of the sigmoid function. We have defined a fixed number of threads per block and the number of blocks is calculated from the size of the layer divided by the number of threads.…”

Speculative segmented sum for sparse matrix-vector multiplication on heterogeneous processors

“…Thus more evaluation criteria, such as format conversion cost and memory footprint, must be taken into consideration. Secondly, when the SpMV operation is used with other sparse building blocks (e.g., sparse matrix-matrix multiplication [11]) that require basic storage formats, using the all-new formats is less feasible.…”