Lower Bounds for the Number of Repetitions in 2D Strings

Paweł Gawrychowski; Samah Ghazawi; Gad M. Landau

doi:10.1007/978-3-030-86692-1_15

Lower Bounds for the Number of Repetitions in 2D Strings

Paweł Gawrychowski, Samah Ghazawi, Gad M. Landau

Department of Computer Science

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

Abstract

A 2D string is simply a 2D array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs. First, we construct an infinite family of n× n 2D strings with Ω(n³) distinct tandems. Second, we construct an infinite family of n× n 2D strings with Ω(n²log n) distinct quartics. Third, we construct an infinite family of n× n 2D strings with Ω(n²log n) runs. This resolves an open question of Charalampopoulos, Radoszewski, Rytter, Waleń, and Zuba [ESA 2020], who asked if the number of distinct quartics and runs in an n× n 2D string is O(n²).

Original language	English
Title of host publication	String Processing and Information Retrieval - 28th International Symposium, SPIRE 2021, Proceedings
Editors	Thierry Lecroq, Hélène Touzet
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	179-192
Number of pages	14
ISBN (Print)	9783030866914
DOIs	https://doi.org/10.1007/978-3-030-86692-1_15
State	Published - 2021
Event	28th International Symposium on String Processing and Information Retrieval, SPIRE 2021 - Virtual, Online Duration: 4 Oct 2021 → 6 Oct 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12944 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	28th International Symposium on String Processing and Information Retrieval, SPIRE 2021
City	Virtual, Online
Period	4/10/21 → 6/10/21

Bibliographical note

Funding Information:
P. Gawrychowski—Partially supported by the Bekker programme of the Polish National Agency for Academic Exchange (PPN/BEK/2020/1/00444). S. Ghazawi and G. 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:
© 2021, Springer Nature Switzerland AG.

Keywords

2D strings
Quartics
Runs
Tandems

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

Access to Document

10.1007/978-3-030-86692-1_15

Cite this

Gawrychowski, P., Ghazawi, S., & Landau, G. M. (2021). Lower Bounds for the Number of Repetitions in 2D Strings. In T. Lecroq, & H. Touzet (Eds.), String Processing and Information Retrieval - 28th International Symposium, SPIRE 2021, Proceedings (pp. 179-192). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12944 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-86692-1_15

Gawrychowski, Paweł ; Ghazawi, Samah ; Landau, Gad M. / Lower Bounds for the Number of Repetitions in 2D Strings. String Processing and Information Retrieval - 28th International Symposium, SPIRE 2021, Proceedings. editor / Thierry Lecroq ; Hélène Touzet. Springer Science and Business Media Deutschland GmbH, 2021. pp. 179-192 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A 2D string is simply a 2D array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs. First, we construct an infinite family of n× n 2D strings with Ω(n3) distinct tandems. Second, we construct an infinite family of n× n 2D strings with Ω(n2log n) distinct quartics. Third, we construct an infinite family of n× n 2D strings with Ω(n2log n) runs. This resolves an open question of Charalampopoulos, Radoszewski, Rytter, Wale{\'n}, and Zuba [ESA 2020], who asked if the number of distinct quartics and runs in an n× n 2D string is O(n2).",

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Gawrychowski, P, Ghazawi, S & Landau, GM 2021, Lower Bounds for the Number of Repetitions in 2D Strings. in T Lecroq & H Touzet (eds), String Processing and Information Retrieval - 28th International Symposium, SPIRE 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12944 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 179-192, 28th International Symposium on String Processing and Information Retrieval, SPIRE 2021, Virtual, Online, 4/10/21. https://doi.org/10.1007/978-3-030-86692-1_15

Lower Bounds for the Number of Repetitions in 2D Strings. / Gawrychowski, Paweł; Ghazawi, Samah; Landau, Gad M.
String Processing and Information Retrieval - 28th International Symposium, SPIRE 2021, Proceedings. ed. / Thierry Lecroq; Hélène Touzet. Springer Science and Business Media Deutschland GmbH, 2021. p. 179-192 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12944 LNCS).

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

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Gawrychowski P, Ghazawi S, Landau GM. Lower Bounds for the Number of Repetitions in 2D Strings. In Lecroq T, Touzet H, editors, String Processing and Information Retrieval - 28th International Symposium, SPIRE 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 179-192. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-86692-1_15