Date of Award
6-1-2001
Document Type
Thesis (Undergraduate)
Department or Program
Department of Computer Science
First Advisor
Tom Cormen
Abstract
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.
Recommended Citation
Fineman, Jeremy T., "Optimizing the Dimensional Method for Performing Multidimensional, Multiprocessor, Out-of-Core FFTs" (2001). Dartmouth College Undergraduate Theses. 17.
https://digitalcommons.dartmouth.edu/senior_theses/17
Comments
Originally posted in the Dartmouth College Computer Science Technical Report Series, number TR2001-402.