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

Abstract

We present an algorithm for general sparse matrix-matrix multiplication (SpGEMM) on many-core architectures, such as GPUs. SpGEMM is implemented by iterative row merging, similar to merge sort, except that elements with duplicate column indices are aggregated on the fly. The main kernel merges small numbers of sparse rows at once using subwarps of threads to realize an early compression effect which reduces the overhead of global memory accesses. The performance is compared with a parallel CPU implementation as well as with three GPU-based implementations. Measurements performed for computing the matrix square for 21 sparse matrices show that the proposed method consistently outperforms the other methods. Analysis showed that the performance is achieved by utilizing the compression effect and the GPU caching architecture. An improved performance was also found for computing Galerkin products which are required by algebraic multigrid solvers. The performance was particularly good for seven-point stencil matrices arising in the context of diffuse optical imaging and the improved performance allows one to perform image reconstruction at higher resolution using the same computational resources.

Hybrid µCT-FMT imaging and image analysis

“…We derive the scattering map by automated segmentation of the µCT data and assigning known scattering coefficients of several tissue types (lung, bone, skin, fat, and remaining soft tissue) 24 . Subsequently, we reconstruct an absorption map from the optical raw data which is particularly important for well-perfused organs such as the heart and the liver 13,20 .…”

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

“…There has been a flurry of activity in developing algorithms and implementations of SpGEMM for Graphics Processing Units (GPUs). Among those, the algorithm of Gremse et al [26] uses the row-wise formulation of SpGEMM. By contrast, Dalton et al [18] uses the data-parallel ESC (expansion, sorting, and contraction) formulation, which is based on outer products.…”

A framework for general sparse matrix–matrix multiplication on GPUs and heterogeneous processors

“…The single precision and double precision absolute performance of the SpGEMM algorithms that compute C = A 2 are shown in Figures 8 and 9, respectively. Four GPU methods from CUSP v0.4.0, cuSPARSE v6.5, RMerge [16] and bhSPARSE are evaluated on three GPUs: nVidia GeForce GTX Titan Black, nVidia GeForce GTX 980 and AMD Radeon R9 290X. One CPU method in Intel MKL v11.0 is evaluated on Intel Xeon E5-2630 CPU.…”

“…Previous GPU SpGEMM methods [2,12,13,14,15,16] have proposed a few solutions for the above problems and demonstrated relatively good time and space complexity. However, the experimental results showed that they either only work best for fairly regular sparse matrices [12,13,16], or bring extra high memory overhead for matrices with some specific sparsity structures [2,14,15]. Moreover, in the usual sense, none of these methods can constantly outperform well optimized SpGEMM approach [17] for multicore CPUs.…”