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Reconstructing Parameterized Strings from Parameterized Suffix and LCP Arrays

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String Processing and Information Retrieval (SPIRE 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13617))

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Abstract

Reconstructing input from a data structure entails determining whether an instance of the data structure is in fact valid or not, and if valid, discovering the underlying data that it represents. In this paper we consider the parameterized suffix array (pSA) along with its corresponding parameterized longest-common-prefix (pLCP) array and solve the following problem. Given two arrays of numbers as input, A and P, does there exist a parameterized string S such that A is its pSA and P is its pLCP array? If the answer is positive, our algorithm produces a string S whose pSA is A and whose pLCP array is P. Although the naive approach would have to consider an exponential number of possibilities for such a string S, our algorithm’s time complexity is only \(O(n^2)\) for input arrays of size n.

A. Amir—Partially supported by Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF) and Israel Science Foundation Grant 1475-18.

C. Guerra—Partially supported by BSF Grant No. 2018141.

G. M. Landau—Partially supported by Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF) and Israel Science Foundation Grant 1475-18.

D. Sokol—Partially supported by BSF Grant No. 2018141.

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Author information

Authors and Affiliations

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

    Amihood Amir

  2. College of Computing, Georgia Institute of Technology, 801 Atlantic Drive, Atlanta, GA, 30318, USA

    Amihood Amir & Concettina Guerra

  3. Cheriton School of Computer Science, Waterloo University, Waterloo, Canada

    Eitan Kondratovsky

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

    Gad M. Landau

  5. NYU Tandon School of Engineering, New York University, Brooklyn, NY, USA

    Gad M. Landau

  6. Department of Mathematics and Computer Science, Kingsborough Community College of the City University of New York, Brooklyn, NY, USA

    Shoshana Marcus

  7. Department of Computer and Information Science, Brooklyn College and The Graduate Center, City University of New York, Brooklyn, NY, USA

    Dina Sokol

Authors
  1. Amihood Amir
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  2. Concettina Guerra
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  3. Eitan Kondratovsky
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  4. Gad M. Landau
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  5. Shoshana Marcus
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  6. Dina Sokol
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Corresponding author

Correspondence to Shoshana Marcus .

Editor information

Editors and Affiliations

  1. Universidad Técnica Federico Santa María, Valparaíso, Chile

    Diego Arroyuelo

  2. Universidad de Chile, Santiago, Chile

    Barbara Poblete

A Appendix

A Appendix

Fig. 1.
figure 1

(left) The input p-suffix and pLCP arrays. (center) The Left-Table is constructed with unknown placeholders representing mismatch at the end of the pLCPs depicted in red. (right) The Left-Table after using Algorithm  1 to resolve the unknowns in red and updating other occurrences of the same unknowns, to maintain consistency. (Color figure online)

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Fig. 2.
figure 2

(left) We initially fill the Right-Table by copying p-suffixes from the Left-Table into their places in the Right-Table. The unknown placeholders we are able to resolve from context within their columns are shown in yellow. The remaining unknown placeholders are colored orange. (right) The completed Right-Table and two different possible p-strings corresponding to it. (Color figure online)

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Amir, A., Guerra, C., Kondratovsky, E., Landau, G.M., Marcus, S., Sokol, D. (2022). Reconstructing Parameterized Strings from Parameterized Suffix and LCP Arrays. In: Arroyuelo, D., Poblete, B. (eds) String Processing and Information Retrieval. SPIRE 2022. Lecture Notes in Computer Science, vol 13617. Springer, Cham. https://doi.org/10.1007/978-3-031-20643-6_5

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  • DOI: https://doi.org/10.1007/978-3-031-20643-6_5

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-20643-6

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