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Sparse matrix--matrix multiplication (SpGEMM) is a key operation in numerous areas from information to the physical sciences. Implementing SpGEMM efficiently on throughput-oriented processors, such as the graphics processing unit (GPU), requires the programmer to expose substantial fine-grained parallelism while conserving the limited off-chip memory bandwidth. Balancing these concerns, we decompose the SpGEMM operation into three highly parallel phases: expansion, sorting, and contraction, and introduce a set of complementary bandwidth-saving performance optimizations. Our implementation is fully general and our optimization strategy adaptively processes the SpGEMM workload row-wise to substantially improve performance by decreasing the work complexity and utilizing the memory hierarchy more effectively.
Dalton et al. (Mon,) studied this question.