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Double String Tandem Repeats

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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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Notes

  1. In DNA there are specific relationships between corresponding bases, while our definition of a double string does not imply any such relationship.

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Funding

The authors A. Amir and G. M. Landau have been partially supported by Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF) and Israel Science Foundation Grant 1475-18. D. Sokol was also partially supported by BSF Grant No. 2018141. S. Marcus was partially supported by the Professional Staff Congress City University of New York Research Award 63164-00 51.

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Authors and Affiliations

  1. Department of Computer Science, Bar Ilan University, 52900, Ramat-Gan, Israel

    Amihood Amir

  2. Department of Computer Science, Holon Institude of Technology, Golomb St 52, 5810201, Holon, Israel

    Ayelet Butman

  3. Department of Computer Science, University of Haifa, 31905, Haifa, Israel

    Gad M. Landau

  4. NYU Tandon School of Engineering, New York University, Six MetroTech Center, Brooklyn, NY, 11201, USA

    Gad M. Landau

  5. Department of Mathematics and Computer Science, Kingsborough Community College of the City University of New York, 2001 Oriental Boulevard, Brooklyn, NY, 11235, USA

    Shoshana Marcus

  6. Department of Computer and Information Science, Brooklyn College of the City University of New York, 2900 Bedford Avenue, Brooklyn, NY, 11210, USA

    Dina Sokol

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  1. Amihood Amir
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  2. Ayelet Butman
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  3. Gad M. Landau
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  4. Shoshana Marcus
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  5. Dina Sokol
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Correspondence to Dina Sokol.

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Amir, A., Butman, A., Landau, G.M. et al. Double String Tandem Repeats. Algorithmica 85, 170–187 (2023). https://doi.org/10.1007/s00453-022-01016-9

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  • DOI: https://doi.org/10.1007/s00453-022-01016-9

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