## 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.

Original language | English |
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Article number | 114230 |

Journal | Theoretical Computer Science |

Volume | 981 |

DOIs | |

State | Published - 4 Jan 2024 |

### Bibliographical note

Publisher Copyright:© 2023

### Funding

Partially supported by Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF) and Israel Science Foundation Grant 22-168-23.Partially supported by the Professional Staff Congress of the City University of New York (PSC-CUNY) grant number 66557-00 54.Partially supported by Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF).The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Dina Sokol, Amihood Amir, Gad M. Landau reports financial support was provided by Binational Science Foundation.

Funders | Funder number |
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City University of New York | |

Professional Staff Congress and City University of New York | 66557-00 54 |

United States-Israel Binational Science Foundation | |

Israel Science Foundation | 22-168-23 |

## Keywords

- Longest common prefix array
- Parameterized strings
- Strings
- Suffix array