Deriving Array Distributions by Optimization Techniques

The paper presents a new method to derive data distributions for parallel computers with distributed memory organization by a mathematical optimization technique. Prerequisites for this approach are a parameterized data distribution and a rigorous performance prediction technique that allows us to derive runtime formulas containing the parameters of the data distribution. A mathematical optimization technique can then be used to determine the parameters in such a way that the total runtime is minimized, thus also minimizing the communication overhead and the load imbalance penalty. The method is demonstrated by using it to determine a data distribution for the LU decomposition of a matrix.