Efficient Parallel Scheduling for Sparse Triangular Solvers

Abstract: We develop and analyze new scheduling algorithms for solving sparse triangular linear systems (SpTRSV) in parallel. Our approach produces highly efficient synchronous schedules for the forward- and backward-substitution algorithm. Compared to state-of-the-art baselines HDagg and SpMP, we achieve a $3.32 \times$ and $1.42 \times$ geometric-mean speed-up, respectively. We achieve this by obtaining an up to $12.07 \times$ geometric-mean reduction in the number of synchronization barriers over HDagg, whilst maintaining a balanced workload, and by applying a matrix reordering step for locality. We show that our improvements are consistent across a variety of input matrices and hardware architectures.