PDF e-Pub

## Section: New Results

### Efficient and effective sparse tensor reordering

This paper formalizes the problem of reordering a sparse tensor to improve the spatial and temporal locality of operations with it, and proposes two reordering algorithms for this problem, which we call BFS-MCS and Lexi-Order. The BFS-MCS method 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. We show the effects of these schemes within the context of a widely used tensor computation, the Candecomp/Parafac decomposition (CPD), when storing the tensor in three previously proposed sparse tensor formats: coordinate (COO), compressed sparse fiber (CSF), and hierarchical coordinate (HiCOO). A new partition-based superblock scheduling is also proposed for HiCOO format to improve load balance. On modern multicore CPUs, we show Lexi-Order obtains up to 4.14$×$ speedup on sequential HiCOO-Mttkrp and 11.88$×$ speedup on its parallel counterpart. The performance of COO-and CSF-based Mttkrps also improves. Our two reordering methods are more effective than state-of-the-art approaches.

This work appears in the proceedings of ICS2019 [21].