Efficient Parallel Sparse Tensor Contraction

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-sparse matrix multiplication (SpGEMM) operation. Therefore, SpGETT can be performed by first converting the input tensors into matrices, then invoking high performance variants 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 without matrix formulation. We discuss the building blocks in both approaches and formulate a hashing-based method to avoid costly search or 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 article. We evaluate the methods on real world tensors by contracting a tensor with itself along varying 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.