Optimal communication algorithms for regular decompositions on the hypercube
C3P Proceedings of the third conference on Hypercube concurrent computers and applications: Architecture, software, computer systems, and general issues - Volume 1
What have we learnt from using real parallel machines to solve real problems?
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
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We have implemented one of the Fast Fourier Transform algorithms, the Prime Factor algorithm (PFA), on the hypercube. On sequential computers, the PFA and other discrete Fourier transforms (DFT) such as the Winograd algorithm (WFA) are known to be very efficient. However, both algorithms require full data shuffling and are thus challenging to any distributed memory parallel computers. We use a concurrent communication algorithm, called the Crystal_Router for communicating shuffled data. We will show that the speed gained in reduced arithmetic compared to binary FFT is sufficient to overcome the extra communication requirement up to a certain number of processors. Beyond this point the standard Cooley-Tukey FFT algorithm has the best performance. We comment briefly on the application of the DFT to signal processing in synthetic aperture radar (SAR).