Efficient Parallel Scheduling for Sparse Triangular Solvers

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.