Adaptive Level Binning: A New Algorithm for Solving Sparse Triangular Systems

Abstract

Sparse triangular solve (SpTRSV) is an important scientific kernel used in several applications such as preconditioners for Krylov methods. Parallelizing SpTRSV on multi-core systems is challenging since it exhibits limited parallelism due to computational dependencies and introduces high parallelization overhead due to finegrained and unbalanced nature of workloads. We propose a novel method, named Adaptive Level Binning (ALB), that addresses these challenges by eliminating redundant synchronization points and adapting the work granularity with an efficient load balancing strategy. Similar to the commonly used level-set methods for solving SpTRSV, ALB constructs level-sets of rows, where each level can be computed in parallel. Differently, ALB bins rows to levels adaptively and reduces redundant dependencies between rows. On an Intel® Xeon® Gold 6148 processor and NVIDIA® Tesla V100 GPU, ALB obtains 1.83x speedup on average and up to 5.28x speedup over Intel MKL and, over NVIDIA cuSPARSE, an average speedup of 2.80x and a maximum speedup of 39.40x for 29 matrices selected from Suite Sparse Matrix Collection.