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Finding Maximum and Minimum Size Matrices: The Algorithmic Complexity of Coding Challenges

Authors Abdelrahman Abdelmonsef , Xingyu Dong , Daniel Průša , Michael Wehar , Chen Xu

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LIPIcs.FUN.2026.1.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Pattern Matching
  • Matrices
  • Discrete Algorithms

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Abstract

We investigate coding challenge problems related to finding a maximum (or minimum) size match for a predetermined two-dimensional pattern. We improve upon known runtime results by introducing new algorithms and refining existing algorithmic techniques. First, we present our main result which introduces a nearly quadratic time algorithm for the problem of finding a rectangular block within a matrix of maximum (or minimum) size containing only positive border entries which improves the prior cubic time solution. Then, we introduce a quadratic time and linear space algorithm for the problem of finding all rectangular blocks containing only positive border and empty interior entries. Finally, we present a log(n) factor improvement for detecting the largest length such that all square blocks in a matrix have their sums bounded by a given number.

Cite As Get BibTex

Abdelrahman Abdelmonsef, Xingyu Dong, Daniel Průša, Michael Wehar, and Chen Xu. Finding Maximum and Minimum Size Matrices: The Algorithmic Complexity of Coding Challenges. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 1:1-1:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.1

Author Details

Abdelrahman Abdelmonsef
  • Department of Computer Science, Swarthmore College, PA, USA
Xingyu Dong
  • Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, USA
Daniel Průša
  • Faculty of Electrical Engineering, Czech Technical University, Prague, Czech Republic
Michael Wehar
  • Department of Computer Science, Bryn Mawr College, PA, USA
Chen Xu
  • Department of Computer Science and Engineering, University at Buffalo, NY, USA

Acknowledgements

Preliminary research was pursued by the 1st, 2nd, 4th, and 5th authors in collaboration with the Algorithms Research Group at Swarthmore College during Spring and Fall 2022. We would especially like to thank and recognize the helpful discussions with B. Xiang, D. Yang, E. Brickner, J. Mancini, J. Swernofsky, N. Almadbooh, and all 19 individuals who participated in the Algorithms Research Group. In addition, we would like to thank K. Regan as well as anonymous reviewers for helpful suggestions.

References

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