Adaptive Level Binning

A novel graph transformation strategy for optimizing SpTRSV on CPUs

“…A negative change in the ALC indicates that for some rows the number of dependencies and thus their row costs have decreased by rewriting them. This is possible for rows having transitive edges 5 since they have common parents. The last column indicates the change in the total cost of the computations.…”

“…The sparsity pattern of the matrix can complicate load balancing further. In a previous work, 5 we have shown how the number of threads active in a level can fluctuate throughout the levels.…”

“…The sparsity pattern of the matrix can complicate load balancing further. In a previous work, 5 we have shown how the number of threads active in a level can fluctuate throughout the levels. Unless partitioning of the rows are made with some another approach such as the equation rewriting approach, some threads tend to stay idle within thin levels.…”

“…Although a few, hybrid implementations of level set and synchronization-free methods for CPUs exist in the literature. 5,26 Both works aim to reduce synchronization points for SpTRSV on CPUs, eliminating unnecessary dependencies.…”

“…Sparse triangular solve (SpTRSV) is an important building block to several linear algebra systems such as iterative methods, 1‐3 preconditioners for sparse iterative solvers 3 and least‐squares problems 4 . Although optimizing SpTRSV on parallel architectures has been studied extensively, it remains a challenging problem due to the following reasons: (1) Dependencies between computations result in limited parallelism, (2) Computations are irregular in nature due to the sparsity structure of the matrix: workloads assigned to threads can be fine‐grained and they vary in granularity, (3) Due to challenges 1 and 2, load balancing and synchronization become difficult 5 …”