Brief Announcement: Faster Stencil Computations using Gaussian Approximations

Zafar Ahmad, Rezaul Chowdhury, Rathish Das, Pramod Ganapathi, Aaron Gregory, Yimin Zhu

Abstract: Stencil computations are widely used to simulate the change of state of physical systems. The current best algorithm for performing aperiodic linear stencil computations on a d (≥ 1)-dimensional grid of size N for T timesteps does Θ(TN1-1/d+N Log N) work. We introduce novel techniques based on random walks and Gaussian approximations for an asymptotic improvement of this work bound for a class of linear stencils. We also improve the span (i.e., parallel running time on an unbounded number of processors) asymptotically from the current state of the art.