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Order-Preserving Squares in Strings

Authors Paweł Gawrychowski , Samah Ghazawi, Gad M. Landau

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Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • repetitions
  • distinct squares
  • order-isomorphism

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Abstract

An order-preserving square in a string is a fragment of the form uv where u ≠ v and u is order-isomorphic to v. We show that a string w of length n over an alphabet of size σ contains 𝒪(σn) order-preserving squares that are distinct as words. This improves the upper bound of 𝒪(σ²n) by Kociumaka, Radoszewski, Rytter, and Waleń [TCS 2016]. Further, for every σ and n we exhibit a string with Ω(σn) order-preserving squares that are distinct as words, thus establishing that our upper bound is asymptotically tight. Finally, we design an 𝒪(σn) time algorithm that outputs all order-preserving squares that occur in a given string and are distinct as words. By our lower bound, this is optimal in the worst case.

Cite As Get BibTex

Paweł Gawrychowski, Samah Ghazawi, and Gad M. Landau. Order-Preserving Squares in Strings. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CPM.2023.13

Author Details

Paweł Gawrychowski
  • Institute of Computer Science, University of Wrocław, Poland
Samah Ghazawi
  • Department of Computer Science, University of Haifa, Israel
Gad M. Landau
  • Department of Computer Science, University of Haifa, Israel
  • Department of Computer Science and Engineering, NYU Tandon School of Engineering, New York University, Brooklyn, NY, USA

Funding

  • Ghazawi, Samah: partially supported by the Israel Science Foundation grant 1475/18, and Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF).
  • Landau, Gad M.: partially supported by the Israel Science Foundation grant 1475/18, and Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF).

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