Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2503.18974

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

Swastik Bhandari
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

cs.DSmath.OC

Keep this discovery

BibTeXRIS

Swastik Bhandari. 2025-03-22. An Efficient Frequency-Based Approach for Maximal Square Detection in Binary Matrices. https://arxiv.org/abs/2503.18974

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗
arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗