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DOI: 10.4230/LIPIcs.CPM.2020.3

Double String Tandem Repeats

Authors: Amihood Amir, Ayelet Butman, Gad M. Landau, Shoshana Marcus, and Dina Sokol

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract

A tandem repeat is an occurrence of two adjacent identical substrings. In this paper, we introduce the notion of a double string, which consists of two parallel strings, and we study the problem of locating all tandem repeats in a double string. The problem introduced here has applications beyond actual double strings, as we illustrate by solving two different problems with the algorithm of the double string tandem repeats problem. The first problem is that of finding all corner-sharing tandems in a 2-dimensional text, defined by Apostolico and Brimkov. The second problem is that of finding all scaled tandem repeats in a 1d text, where a scaled tandem repeat is defined as a string UU' such that U' is discrete scale of U. In addition to the algorithms for exact tandem repeats, we also present algorithms that solve the problem in the inexact sense, allowing up to k mismatches. We believe that this framework will open a new perspective for other problems in the future.

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Amihood Amir, Ayelet Butman, Gad M. Landau, Shoshana Marcus, and Dina Sokol. Double String Tandem Repeats. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 3:1-3:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{amir_et_al:LIPIcs.CPM.2020.3,
  author =	{Amir, Amihood and Butman, Ayelet and Landau, Gad M. and Marcus, Shoshana and Sokol, Dina},
  title =	{{Double String Tandem Repeats}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{3:1--3:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.3},
  URN =		{urn:nbn:de:0030-drops-121283},
  doi =		{10.4230/LIPIcs.CPM.2020.3},
  annote =	{Keywords: double string, tandem repeat, 2-dimensional, scale}
}

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DOI: 10.4230/LIPIcs.ESA.2018.2

Two-Dimensional Maximal Repetitions

Authors: Amihood Amir, Gad M. Landau, Shoshana Marcus, and Dina Sokol

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

Maximal repetitions or runs in strings have a wide array of applications and thus have been extensively studied. In this paper, we extend this notion to 2-dimensions, precisely defining a maximal 2D repetition. We provide initial bounds on the number of maximal 2D repetitions that can occur in a matrix. The main contribution of this paper is the presentation of the first algorithm for locating all maximal 2D repetitions in a matrix. The algorithm is efficient and straightforward, with runtime O(n^2 log n log log n+ rho log n), where n^2 is the size of the input, and rho is the number of 2D repetitions in the output.

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Amihood Amir, Gad M. Landau, Shoshana Marcus, and Dina Sokol. Two-Dimensional Maximal Repetitions. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{amir_et_al:LIPIcs.ESA.2018.2,
  author =	{Amir, Amihood and Landau, Gad M. and Marcus, Shoshana and Sokol, Dina},
  title =	{{Two-Dimensional Maximal Repetitions}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{2:1--2:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.2},
  URN =		{urn:nbn:de:0030-drops-94652},
  doi =		{10.4230/LIPIcs.ESA.2018.2},
  annote =	{Keywords: pattern matching algorithms, repetitions, periodicity, two-dimensional}
}

Document

DOI: 10.4230/LIPIcs.CPM.2016.19

Finding Maximal 2-Dimensional Palindromes

Authors: Sara Geizhals and Dina Sokol

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract

This paper extends the problem of palindrome searching into a higher dimension, addressing two definitions of 2D palindromes. The first definition implies a square, while the second definition (also known as a centrosymmetric factor), can be any rectangular shape. We describe two algorithms for searching a 2D text for maximal palindromes, one for each type of 2D palindrome. The first algorithm is optimal; it runs in linear time, on par with Manacher's linear time 1D palindrome algorithm. The second algorithm searches a text of size n_1 x n_2 (n_1 >= n_2) in O(n_2) time for each of its n_1 x n_2 positions. Since each position may have up to O(n_2) maximal palindromes centered at that location, the second result is also optimal in terms of the worst-case output size.

Cite as

Sara Geizhals and Dina Sokol. Finding Maximal 2-Dimensional Palindromes. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 19:1-19:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{geizhals_et_al:LIPIcs.CPM.2016.19,
  author =	{Geizhals, Sara and Sokol, Dina},
  title =	{{Finding Maximal 2-Dimensional Palindromes}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{19:1--19:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.19},
  URN =		{urn:nbn:de:0030-drops-60752},
  doi =		{10.4230/LIPIcs.CPM.2016.19},
  annote =	{Keywords: palindrome, pattern matching, 2-Dimensional, centrosymmetric factor}
}

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Documents authored by Sokol, Dina

Double String Tandem Repeats

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Two-Dimensional Maximal Repetitions

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Finding Maximal 2-Dimensional Palindromes

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