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Better Indexing for Rectangular Pattern Matching

Authors Paweł Gawrychowski , Adam Górkiewicz

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Pattern matching
Keywords
  • 2D strings
  • pattern matching
  • string indexing

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Abstract

We revisit the complexity of building, given a two-dimensional string of size n, an indexing structure that allows locating all k occurrences of a two-dimensional pattern of size m. While a structure of size 𝒪(n) with query time 𝒪(m+k) is known for this problem under the additional assumption that the pattern is a square [Giancarlo, SICOMP 1995], a popular belief was that for rectangular patterns one cannot achieve such (or even similar) bounds, due to a lower bound for a certain natural class of approaches [Giancarlo, WADS 1993]. We show that, in fact, it is possible to construct a very simple structure of size 𝒪(nlog n) that supports such queries for any rectangular pattern in 𝒪(m+klog^{ε}n) time, for any ε > 0.

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Paweł Gawrychowski and Adam Górkiewicz. Better Indexing for Rectangular Pattern Matching. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 33:1-33:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.33

Author Details

Paweł Gawrychowski
  • Institute of Computer Science, University of Wrocław, Poland
Adam Górkiewicz
  • Institute of Computer Science, University of Wrocław, Poland

Funding

Partially supported by the Polish National Science Centre grant number 2023/51/B/ST6/ 01505.

Acknowledgements

We would like to thank Itai Boneh and Panagiotis Charalampopoulos for participating in the initial discussion.

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