Efficient Generation of Binary Magic Squares
This provides a theoretical solution for generating binary magic squares, which is a niche mathematical/computational problem.
The authors developed an algorithm for generating Binary Magic Squares (square binary matrices with equal row and column sums) with optimal theoretical complexity, and extended it to handle non-square matrices with formal existence conditions.
We propose a simple algorithm for generating Binary Magic Squares (BMS), i.e., square binary matrices where the sum of all rows and all columns are equal. We show by induction that our algorithm always returns valid BMS with optimal theoretical complexity. We then extend our study to non-square Binary Magic Squares, formalize conditions on the sum of rows and columns for these BMS to exist, and show that a slight variant of our first algorithm can generate provably generate them. Finally, we publicly release two implementations of our algorithm as Python packages, including one that can generate several BMS in parallel using GPU acceleration.