An Algebraic Theory for Regular Data Mappings on Parallel Computers

An algebraic theory for regular data mappings of multidimensional meshes is introduced. Mappings with nice algebraic properties are discussed. These include families of mesh{to{mesh permutations and reshapes of a mesh onto meshes of diierent shape, and are useful for expressing various regular algorithms such as e.g. dense matrix operations, fast Fourier{ and wavelet{transforms, convolutions and multigrid techniques. The algebraic approach is nally used in the construction of fast optimal routing algorithms for the resulting permutations on a wide range of parallel computer networks.

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