Parallel Sparse Matrix Vector Multiplication using greedy extraction of boxes

Parallel Sparse Matrix Vector Multiplication (PSpMV) is a compute intensive kernel used in iterative solvers like Conjugate Gradient, GMRES and Lanzcos. Numerous attempts at optimizing this function have been made that require fine tuning of many hardware and software parameters to achieve optimal performance. We attempt to offer a simple framework that involves (i) Employing a greedy algorithm to extract variable-sized dense sub matrices without zeroes filled in, (ii) Partitioning the sparse matrix in a load balanced manner and maintaining partial information at each node, and (iii) Overlapping communication with computation. Using the aforementioned, we reduce memory traffic and hide communication latencies, and hope to inherently achieve improved cache and register utilization. This paper reports the performance improvements of PSpMV as such and when used in Preconditioned Conjugate Gradient (PCG).