Linear Time Reconstruction of Parameterized Strings from Parameterized Suffix and LCP Arrays for Constant-Sized Alphabets

Amihood Amir; Eitan Kondratovsky; Shoshana Marcus; Dina Sokol

doi:10.1007/978-3-031-72200-4_1

Linear Time Reconstruction of Parameterized Strings from Parameterized Suffix and LCP Arrays for Constant-Sized Alphabets

Amihood Amir, Eitan Kondratovsky, Shoshana Marcus, Dina Sokol

Department of Computer Science

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

Abstract

A parameterized string (p-string) is a string that can contain two kinds of characters, static symbols and parameter characters. Parameterized pattern matching is a form of pattern matching that allows parameters to be renamed by applying a one-to-one function. The parameterized suffix array is a data structure that is useful in efficient parameterized pattern matching when accompanied by the parameterized longest common prefix (LCP) array. Reconstructing input from a given instance of a data structure is the task of determining whether the instance is valid or not, and if valid, producing a plausible set of data that it can represent. In this paper we consider parameterized suffix and LCP arrays and reconstruct a corresponding p-string that they can represent. In previous work, an algorithm can determine in O(n²) time whether a p-string can be constructed to correspond to the input parameterized suffix and LCP arrays of size n. In this work, we develop an algorithm that accomplishes this in O(n) time for constant-sized alphabets, and O(nlogn) time for general alphabets. Furthermore, when reconstruction is possible, we demonstrate that a p-string can be reconstructed over the minimal alphabet in O(n²) time.

Original language	English
Title of host publication	String Processing and Information Retrieval - 31st International Symposium, SPIRE 2024, Proceedings
Editors	Zsuzsanna Lipták, Edleno Moura, Karina Figueroa, Ricardo Baeza-Yates
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	1-15
Number of pages	15
ISBN (Print)	9783031721991
DOIs	https://doi.org/10.1007/978-3-031-72200-4_1
State	Published - 2025
Event	31st International Symposium on String Processing and Information Retrieval, SPIRE 2024 - Puerto Vallarta, Mexico Duration: 23 Sep 2024 → 25 Sep 2024

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14899 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	31st International Symposium on String Processing and Information Retrieval, SPIRE 2024
Country/Territory	Mexico
City	Puerto Vallarta
Period	23/09/24 → 25/09/24

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

Keywords

Longest Common Prefix Array
Parameterized Strings
Reverse Engineering
Strings
Suffix Array

Access to Document

10.1007/978-3-031-72200-4_1

Cite this

Amir, A., Kondratovsky, E., Marcus, S., & Sokol, D. (2025). Linear Time Reconstruction of Parameterized Strings from Parameterized Suffix and LCP Arrays for Constant-Sized Alphabets. In Z. Lipták, E. Moura, K. Figueroa, & R. Baeza-Yates (Eds.), String Processing and Information Retrieval - 31st International Symposium, SPIRE 2024, Proceedings (pp. 1-15). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14899 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-72200-4_1

Amir, Amihood ; Kondratovsky, Eitan ; Marcus, Shoshana et al. / Linear Time Reconstruction of Parameterized Strings from Parameterized Suffix and LCP Arrays for Constant-Sized Alphabets. String Processing and Information Retrieval - 31st International Symposium, SPIRE 2024, Proceedings. editor / Zsuzsanna Lipták ; Edleno Moura ; Karina Figueroa ; Ricardo Baeza-Yates. Springer Science and Business Media Deutschland GmbH, 2025. pp. 1-15 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A parameterized string (p-string) is a string that can contain two kinds of characters, static symbols and parameter characters. Parameterized pattern matching is a form of pattern matching that allows parameters to be renamed by applying a one-to-one function. The parameterized suffix array is a data structure that is useful in efficient parameterized pattern matching when accompanied by the parameterized longest common prefix (LCP) array. Reconstructing input from a given instance of a data structure is the task of determining whether the instance is valid or not, and if valid, producing a plausible set of data that it can represent. In this paper we consider parameterized suffix and LCP arrays and reconstruct a corresponding p-string that they can represent. In previous work, an algorithm can determine in O(n2) time whether a p-string can be constructed to correspond to the input parameterized suffix and LCP arrays of size n. In this work, we develop an algorithm that accomplishes this in O(n) time for constant-sized alphabets, and O(nlogn) time for general alphabets. Furthermore, when reconstruction is possible, we demonstrate that a p-string can be reconstructed over the minimal alphabet in O(n2) time.",

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Amir, A, Kondratovsky, E, Marcus, S & Sokol, D 2025, Linear Time Reconstruction of Parameterized Strings from Parameterized Suffix and LCP Arrays for Constant-Sized Alphabets. in Z Lipták, E Moura, K Figueroa & R Baeza-Yates (eds), String Processing and Information Retrieval - 31st International Symposium, SPIRE 2024, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14899 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 1-15, 31st International Symposium on String Processing and Information Retrieval, SPIRE 2024, Puerto Vallarta, Mexico, 23/09/24. https://doi.org/10.1007/978-3-031-72200-4_1

Linear Time Reconstruction of Parameterized Strings from Parameterized Suffix and LCP Arrays for Constant-Sized Alphabets. / Amir, Amihood; Kondratovsky, Eitan; Marcus, Shoshana et al.
String Processing and Information Retrieval - 31st International Symposium, SPIRE 2024, Proceedings. ed. / Zsuzsanna Lipták; Edleno Moura; Karina Figueroa; Ricardo Baeza-Yates. Springer Science and Business Media Deutschland GmbH, 2025. p. 1-15 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14899 LNCS).

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

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Amir A, Kondratovsky E, Marcus S, Sokol D. Linear Time Reconstruction of Parameterized Strings from Parameterized Suffix and LCP Arrays for Constant-Sized Alphabets. In Lipták Z, Moura E, Figueroa K, Baeza-Yates R, editors, String Processing and Information Retrieval - 31st International Symposium, SPIRE 2024, Proceedings. Springer Science and Business Media Deutschland GmbH. 2025. p. 1-15. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-72200-4_1

Linear Time Reconstruction of Parameterized Strings from Parameterized Suffix and LCP Arrays for Constant-Sized Alphabets

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Keywords

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