BAAS: A Bidirectional Aggregation and Affinity-Aware Scheduling Framework for Parallelizing Sparse Matrix Computations

Parallelizing sparse matrix computations with loop-carried dependencies, such as sparse triangular solve and incomplete factorizations, is critical for scientific computing, yet remains challenging on modern multi-core architectures due to irregular data dependencies. These dependencies complicate task scheduling, making it difficult to maximize data locality, ensure load balance, and minimize synchronization overhead. This paper presents BAAS, a novel framework for shared-memory systems that generates high-performance parallel schedule by addressing these trade-offs. BAAS features two core contributions. First, we propose a Bidirectional Subtree Aggregation scheme that captures both divergent and convergent node patterns to improve data locality and reduce synchronization by grouping strongly dependent nodes. Second, we introduce an Affinity-Aware Scheduling strategy that uses adaptive wavefront coarsening to allocate an appropriate number of threads while merging consecutive parallel bottlenecks, and employs node-thread affinity-aware mapping to assign nodes to threads, minimizing inter-thread synchronizations and maintaining load balance. The experimental results show that BAAS consistently outperforms vendor-libraries and state-of-the-art methods in SpTRSV, SpIC0, and SpILU0, achieving superior efficiency. Furthermore, when integrated into the ICCG iterative solver, BAAS further proves its ability to significantly enhance the end-to-end solver performance.