Eecient Parallel Ffts for Diierent Computational Models Eecient Parallel Ffts for Diierent Computational Models

We select the Fast Fourier Transfrom (FFT) to demonstrate a methodology for deriving the optimal parallel algorithm according to predetermined performance metrics, within a computational model. Following the vector space framework for parallel permutations, we provide a speciication language to capture the algorithm, derive the optimal parallel FFT speciication, compute the arithmetic, memory, communication and load{balance complexity metrics, apply the analytical performance evaluation to PRAM, LPRAM, BSP and LogP computational models, and compare with actual performance results.