Data alignment: transformations to reduce communication on distributed memory architectures

The relative storage, or alignment, of array data in distributed memory critically determines the amount of communication overhead. This paper expresses data alignment in a linear algebraic framework. Aligned data can be viewed as forming a hyperplane in the iteration space. This allows the quantification of data alignment and the determination of the existence of transformations and the determination of the existence of transformations to reduce nonlocal access. This has led to a new alignment transformation which is applicable to a wider class of problems than existing techniques. The global impact of such transformations are discussed as is the effect of alignment on partitioning.<>