Optimal orthogonal tiling

Iteration space tiling is a common strategy used by parallelizing compilers and in performance tuning of parallel codes. We address the problem of determining the tile size that minimizes the total execution time. We restrict our attention to orthogonal tiling—uniform dependency programs with (hyper) parallelepiped shaped iteration domains which can be tiled with hyperplanes parallel to the domain boundaries. Our formulation includes many machine and program models used in the literature, notably the Bsp programming model. We resolve the optimization problem analytically, yielding a closed form solution.