Determining an out-of-Core FFT Decomposition Strategy for Parallel Disks by Dynamic Programming

Abstract

We present an out-of-core FFT algorithm based on the in-core FFT method developed by Swarztrauber. Our algorithm uses a recursive divide-and-conquer strategy, and each stage in the recursion presents several possibilities for how to split the problem into subproblems. We give a recurrence for the algorithm’s I/O complexity on the Parallel Disk Model and show how to use dynamic programming to determine optimal splits at each recursive stage. The algorithm to determine the optimal splits takes only Θ(lg² N) time for an N-point FFT, and it is practical. The out-of-core FFT algorithm itself takes considerably longer.

Supported in part by the National Science Foundation under grant CCR-9625894. Portions of this work were performed while the author was visiting the Institute for Mathematics and its Applications at the University of Minnesota.

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