Effects of Band-K Reordering on Sparse Tensor Formats for Parallel Architectures

Abstract

This thesis presents a background in sparse tensor formats and a study of the effects of Band-K and lexi-ordering on the HiCOO sparse tensor format using the matricized tensor times Khatri-Rao product (MTTKRP). We provide a background of sparse tensors and tensors in general. We cover several foundational sparse tensor formats including CSR, BCSR, and COO, and extensions to those formats HiCOO and CSR-K. Furthermore, we discuss methods of reordering tensors using Band-K and lexi-ordering. Finally, we modify HiParTI to supporting Band-K reordering over slices and benchmark the results against lexi-ordering and natural ordering.