
We investigate the performance of algorithms for sparse tensor-sparse tensor multiplication (SpGeTT). This operation, also called sparse tensor contraction, is a higher order analogue of the sparse matrix-sparsematrix multiplication (SpGeMM) operation. Therefore,SpGeTT can be performed by first converting the input tensors into matrices, then invoking high performancevariants of SpGeMM, and finally reconverting the resultant matrix into a tensor.Alternatively, one can carry out the scalar operations underlying SpGeTT in the realm of tensors withoutmatrix formulation.We discuss the building blocks in both approaches and formulate a hashing-based method to avoid costly searchor redirection operations.We present performance results with the current state-of-the-art SpGeMM-based approaches, existing SpGeTT approaches,and a carefully implemented SpGeTT approach with a new fine-tuned hashing method, proposed in this paper.We evaluate the methods on real world tensors, contracting a tensor with itself along various dimensions.Our proposed hashing-based method for SpGETT consistently outperforms the state-of-the-art method, achieving a 25% reduction in sequential execution time on average and a 21% reduction in parallel execution time on average across a variety of input instances.
tensor contraction, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], hashing
tensor contraction, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], hashing
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