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Sparse matrix-matrix multiplication (SpGEMM) is a widely used kernel invarious graph, scientific computing and machine learning algorithms. In thispaper, we consider SpGEMMs performed on hundreds of thousands of processorsgenerating trillions of nonzeros in the output matrix. Distributed SpGEMM atthis extreme scale faces two key challenges: (1) high communication cost and(2) inadequate memory to generate the output. We address these challenges withan integrated communication-avoiding and memory-constrained SpGEMM algorithmthat scales to 262,144 cores (more than 1 million hardware threads) and canmultiply sparse matrices of any size as long as inputs and a fraction of outputfit in the aggregated memory. As we go from 16,384 cores to 262,144 cores on aCray XC40 supercomputer, the new SpGEMM algorithm runs 10x faster whenmultiplying large-scale protein-similarity matrices.

Communication-Avoiding and Memory-Constrained Sparse Matrix-Matrix Multiplication at Extreme Scale