Dynamic-CSR: A Format for Dynamic Sparse-Matrix Updates

Sparse matrices are a core component in many numerical simulations, and their efficiency is essential to achieving high performance. Dynamic sparse-matrix allocation (insertion) can benefit a number of problems such as sparse-matrix factorization, sparse-matrix-matrix addition, static analysis (e.g., points-to analysis), computing transitive closure, and other graph algorithms. Existing sparse-matrix formats are poorly designed to handle dynamic updates. The compressed sparse-row (CSR) format is fully compact and must be rebuilt after each new entry. Ellpack (ELL) stores a constant number of entries per row, which allows for efficient insertion and sparse matrix-vector multiplication (SpMV) but is memory inefficient and strictly limits row size. The coordinate (COO) format stores a list of entries and is efficient for both memory use and insertion time; however, it is much less efficient at SpMV. Hybrid ellpack (HYB) compromises by using a combination of ELL and COO but degrades in performance as the COO portion fills up. Rows that use the COO portion require it to be completely traversed during every SpMV operation. In this paper we present dynamic compressed sparse row (DCSR), a sparse matrix format that allows for asynchronous dynamic updates, and extend it to an improved SpMM operation. Through the use of DCSR we demonstrate an improved sparse matrix-matrix multiplication (SpMM) algorithm and evaluate it using algebraic multigrid (AMG). AMG is a multigrid operation in which the hierarchy of operators is created from the matrix itself as opposed to the geometry of the mesh. This operation can be expressed in terms of SpMM, SpMV, and primitive parallel operations. DCSR provides significant performance improvements for SpMM through increased memory efficiency due to asynchronous dynamic updates.