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We present an improved version of the Dimensional Method for computing multidimensional Fast Fourier Transforms (FFTs) on a multiprocessor system when the data consist of too many records to fit into memory. Data are spread across parallel disks and processed in sections. We use the Parallel Disk Model for analysis.
The simple Dimensional Method performs the 1-dimensional FFTs for each dimension in term. Between each dimension, an out-of-core permutation is used to rearrange the data to contiguous locations. The improved Dimensional Method processes multiple dimensions at a time.
We show that determining an optimal sequence and groupings of dimensions is NP-complete. We then analyze the effects of two modifications to the Dimensional Method independently: processing multiple dimensions at one time, and processing single dimensions in a different order.
Finally, we show a lower bound on the I/O complexity of the Dimensional Method and present an algorithm that is approximately asymptotically optimal.
Senior Honors Thesis. Advisor: Tom Cormen.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
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Jeremy T. Fineman, "Optimizing the Dimensional Method for Performing Multidimensional, Multiprocessor, Out-of-Core FFTs." Dartmouth Computer Science Technical Report TR2001-402, June 2001.
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