Order-Preserving Squares in Strings

Samah Ghazawi; Gad M. Landau; Paweł Gawrychowski

doi:10.4230/LIPIcs.CPM.2023.13

Order-Preserving Squares in Strings

Samah Ghazawi, Gad M. Landau, Paweł Gawrychowski

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	34th Annual Symposium on Combinatorial Pattern Matching, CPM 2023
Editors	Laurent Bulteau, Zsuzsanna Liptak
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959772761
DOIs	https://doi.org/10.4230/LIPIcs.CPM.2023.13
State	Published - Jun 2023
Event	34th Annual Symposium on Combinatorial Pattern Matching, CPM 2023 - Marne-la-Vallee, France Duration: 26 Jun 2023 → 28 Jun 2023

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	259
ISSN (Print)	1868-8969

Conference

Conference	34th Annual Symposium on Combinatorial Pattern Matching, CPM 2023
Country/Territory	France
City	Marne-la-Vallee
Period	26/06/23 → 28/06/23

Bibliographical note

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

Publisher Copyright:
© 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

Keywords

distinct squares
order-isomorphism
repetitions

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.CPM.2023.13

Cite this

Ghazawi, S., Landau, G. M., & Gawrychowski, P. (2023). Order-Preserving Squares in Strings. In L. Bulteau, & Z. Liptak (Eds.), 34th Annual Symposium on Combinatorial Pattern Matching, CPM 2023 Article 13 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 259). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CPM.2023.13

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title = "Order-Preserving Squares in Strings",

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 Wale{\'n} [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.",

keywords = "distinct squares, order-isomorphism, repetitions",

author = "Samah Ghazawi and Landau, {Gad M.} and Pawe{\l} Gawrychowski",

note = "Funding Information: Funding Samah Ghazawi: partially supported by the Israel Science Foundation grant 1475/18, and Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF). Gad M. Landau: partially supported by the Israel Science Foundation grant 1475/18, and Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF). Publisher Copyright: {\textcopyright} 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.; 34th Annual Symposium on Combinatorial Pattern Matching, CPM 2023 ; Conference date: 26-06-2023 Through 28-06-2023",

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series = "Leibniz International Proceedings in Informatics, LIPIcs",

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Ghazawi, S, Landau, GM & Gawrychowski, P 2023, Order-Preserving Squares in Strings. in L Bulteau & Z Liptak (eds), 34th Annual Symposium on Combinatorial Pattern Matching, CPM 2023., 13, Leibniz International Proceedings in Informatics, LIPIcs, vol. 259, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 34th Annual Symposium on Combinatorial Pattern Matching, CPM 2023, Marne-la-Vallee, France, 26/06/23. https://doi.org/10.4230/LIPIcs.CPM.2023.13

Order-Preserving Squares in Strings. / Ghazawi, Samah; Landau, Gad M.; Gawrychowski, Paweł.
34th Annual Symposium on Combinatorial Pattern Matching, CPM 2023. ed. / Laurent Bulteau; Zsuzsanna Liptak. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2023. 13 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 259).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - Funding Information: Funding Samah Ghazawi: partially supported by the Israel Science Foundation grant 1475/18, and Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF). Gad M. Landau: partially supported by the Israel Science Foundation grant 1475/18, and Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF). Publisher Copyright: © 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

PY - 2023/6

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N2 - 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.

AB - 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.

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A2 - Liptak, Zsuzsanna

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ER -

Order-Preserving Squares in Strings

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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