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DOI: 10.4230/LIPIcs.FUN.2026.1

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

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

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

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.

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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)

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@InProceedings{abdelmonsef_et_al:LIPIcs.FUN.2026.1,
  author =	{Abdelmonsef, Abdelrahman and Dong, Xingyu and Pr\r{u}\v{s}a, Daniel and Wehar, Michael and Xu, Chen},
  title =	{{Finding Maximum and Minimum Size Matrices: The Algorithmic Complexity of Coding Challenges}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{1:1--1:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.1},
  URN =		{urn:nbn:de:0030-drops-257203},
  doi =		{10.4230/LIPIcs.FUN.2026.1},
  annote =	{Keywords: Pattern Matching, Matrices, Discrete Algorithms}
}

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DOI: 10.4230/LIPIcs.STACS.2022.55

Superlinear Lower Bounds Based on ETH

Authors: András Z. Salamon and Michael Wehar

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract

We introduce techniques for proving superlinear conditional lower bounds for polynomial time problems. In particular, we show that CircuitSAT for circuits with m gates and log(m) inputs (denoted by log-CircuitSAT) is not decidable in essentially-linear time unless the exponential time hypothesis (ETH) is false and k-Clique is decidable in essentially-linear time in terms of the graph’s size for all fixed k. Such conditional lower bounds have previously only been demonstrated relative to the strong exponential time hypothesis (SETH). Our results therefore offer significant progress towards proving unconditional superlinear time complexity lower bounds for natural problems in polynomial time.

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András Z. Salamon and Michael Wehar. Superlinear Lower Bounds Based on ETH. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 55:1-55:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{salamon_et_al:LIPIcs.STACS.2022.55,
  author =	{Salamon, Andr\'{a}s Z. and Wehar, Michael},
  title =	{{Superlinear Lower Bounds Based on ETH}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{55:1--55:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.55},
  URN =		{urn:nbn:de:0030-drops-158652},
  doi =		{10.4230/LIPIcs.STACS.2022.55},
  annote =	{Keywords: Circuit Satisfiability, Conditional Lower Bounds, Exponential Time Hypothesis, Limited Nondeterminism}
}

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Documents authored by Wehar, Michael

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

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Superlinear Lower Bounds Based on ETH

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