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arXiv · 2503.05408

Efficient Parallel Scheduling for Sparse Triangular Solvers

Toni Böhnlein·Pál András Papp·Raphael S. Steiner·Christos K. Matzoros·A. N. Yzelman
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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.

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Toni Böhnlein, Pál András Papp, Raphael S. Steiner, Christos K. Matzoros, A. N. Yzelman. 2025-03-07. Efficient Parallel Scheduling for Sparse Triangular Solvers. https://arxiv.org/abs/2503.05408

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