Tiling and processors allocation for three dimensional iteration space

Abstract

We study in this paper the optimal tiling and processors allocation for loops of depth three defined in parallelepiped shaped iteration space. The particularity of the considered class is that the associated dependencies allow orthogonal tiling. We compare ring vs. grid architecture and provide exhaustive numerical experiments on distributed memory machine (Intel Paragon). We also apply the obtained results to solve huge instances of the Bidimensional Knapsack Problem (BKP), which is characterized by 2D non-uniform recurrences. © 1999 Springer-Verlag Berlin Heidelberg.