An Efficient Frequency-Based Approach for Maximal Square Detection in Binary Matrices

Detecting maximal square submatrices of ones in binary matrices is a fundamental problem with applications in computer vision and pattern recognition. While the standard dynamic programming (DP) solution achieves optimal asymptotic complexity, its practical performance suffers from repeated minimum operations and inefficient memory access patterns that degrade cache utilization. To address these limitations, we introduce a novel frequency-based algorithm that employs a greedy approach to track the columnar continuity of ones through an adaptive frequency array and a dynamic thresholding mechanism. Extensive benchmarking demonstrates that the frequency-based algorithm achieves faster performance than the standard DP in 100% of test cases with an average speedup of 3.32x, a maximum speedup of 4.60x, and a minimum speedup of 2.31x across matrices up to 5000x5000 with densities from 0.1 to 0.9. The algorithm's average speedup exceeds 2.5x for all densities and rises to over 3.5x for densities of 0.7 and higher across all matrix sizes. These results demonstrate that the frequency-based approach is a superior alternative to standard DP and opens new possibilities for efficient matrix analysis in performance-critical applications.