2-D SIMD Algorithms In The Perfect Shuffle Networks

This paper studies a set of basic algorithms for SIMD Perfect Shuffle networks. These algorithms where studied in several papers, but for the 1-D case, where the size of the problem N is the same as the number of processors P. For the 2-D case of N = L * P, studied by [GK-80] and [Kr-81], we improve several algorithms, achieving run time O(L + log P) rather than O(L * log P), as N exceeds P. We give non- trivial algorithms for the following 2-D operations: Row-Reduction, Parallel-Prefix, Transpose, Smoothing and Cartesian-Product.