Optimizing the size of array for modern discrete Fourier transform libraries

TL;DR

This paper reformulates the array size optimization for modern discrete Fourier transform libraries as an integer linear programming problem, proposing an efficient recursive algorithm and demonstrating its educational and practical relevance.

Contribution

It introduces an ad hoc recursive algorithm for optimal array size determination and analyzes its complexity, providing a practical approach to a specific integer programming problem.

Findings

Recursive algorithm efficiently finds optimal array sizes.

Complexity of the algorithm is analytically estimated.

The problem serves as an educational example of integer programming.

Abstract

The problem of optimization of the array size for modern discrete Fourier transform libraries is considered and reformulated as an integer linear programming problem. Acceleration of finding an optimal solution using standard freely available library with respect to brute force approach is demonstrated. Ad hoc recursive algorithm of finding the optimal solution is proposed, complexity scaling of the algorithm is estimated analytically. The problem can be used in a linear programming class as an example of purely integer programming problem (continuous linear programming solution has no sense), simple enough to be solved using even interpreting programming languages like Python or Matlab.