Efficient and Effective Sparse Tensor Reordering
This paper proposed two reordering schemes for sparse tensors: BFS-MCS and LEXI-ORDER. BFS-MCS is a Breadth First Search (BFS)-like heuristic approach based on the maximum cardinality search family; LEXI-ORDER is an extension of doubly lexical ordering of matrices to tensors. CANDECOMP/PARAFAC decomposition (CPD) is taken as an example to show their effect on existing three sparse tensor formats for CPUs: coordinate (COO), compressed sparse fiber (CSF), and hierarchical coordinate (HICOO). LEXI-ORDER obtains up to 4.14× speedup on sequential HICOO-MTTKRP and 11.88× speedup on its parallel case. COO- and CSF-MTTKRP also achieves performance improvement in different degree. Our two reordering methods are more efficient and effective than other state-of-the-art reordering methods used in SPLATT.