On Suffix Tree Detection

Amihood Amir; Eitan Kondratovsky; Avivit Levy

doi:10.1007/978-3-031-43980-3_2

On Suffix Tree Detection

Amihood Amir, Eitan Kondratovsky, Avivit Levy

Department of Computer Science

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

3 Scopus citations

Abstract

A suffix tree is a fundamental data structure for string processing and information retrieval, however, its structure is still not well understood. The suffix trees reverse engineering problem, which its research aims at reducing this gap, is the following. Given an ordered rooted tree T with unlabeled edges, determine whether there exists a string w such that the unlabeled-edges suffix tree of w is isomorphic to T. Previous studies on this problem consider the relaxation of having the suffix links as well as assume a binary alphabet. This paper is the first to consider the suffix tree detection problem, in which the relaxation of having suffix links as input is removed. We study suffix tree detection on two scenarios that are interesting per se. We provide a suffix tree detection algorithm for general alphabet periodic strings. Given an ordered tree T with n leaves, our detection algorithm takes $$O(n+|\varSigma |^p)$$ -time, where p is the unknown in advance length of a period that repeats at least 3 times in a string S having a suffix tree structure identical to T, if such S exists. Therefore, it is a polynomial time algorithm if p is a constant and a linear time algorithm if, in addition, the alphabet has a sub-linear size. We also show some necessary (but insufficient) conditions for binary alphabet general strings suffix tree detection. By this we take another step towards understanding suffix trees structure.

Original language	English
Title of host publication	String Processing and Information Retrieval - 30th International Symposium, SPIRE 2023, Proceedings
Editors	Franco Maria Nardini, Nadia Pisanti, Rossano Venturini
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	14-27
Number of pages	14
ISBN (Print)	9783031439797
DOIs	https://doi.org/10.1007/978-3-031-43980-3_2
State	Published - 2023
Event	30th International Symposium on String Processing and Information Retrieval, SPIRE 2023 - Pisa, Italy Duration: 26 Sep 2023 → 28 Sep 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14240 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	30th International Symposium on String Processing and Information Retrieval, SPIRE 2023
Country/Territory	Italy
City	Pisa
Period	26/09/23 → 28/09/23

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

Funding

Partly supported by ISF grant 1475/18 and BSF grant 2018141.

Funders	Funder number
United States-Israel Binational Science Foundation	2018141
Israel Science Foundation	1475/18

Keywords

Periodic string
Reverse engineering
Suffix tree
Suffix tree detection

Access to Document

10.1007/978-3-031-43980-3_2

Cite this

Amir, A., Kondratovsky, E., & Levy, A. (2023). On Suffix Tree Detection. In F. M. Nardini, N. Pisanti, & R. Venturini (Eds.), String Processing and Information Retrieval - 30th International Symposium, SPIRE 2023, Proceedings (pp. 14-27). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14240 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-43980-3_2

Amir, Amihood ; Kondratovsky, Eitan ; Levy, Avivit. / On Suffix Tree Detection. String Processing and Information Retrieval - 30th International Symposium, SPIRE 2023, Proceedings. editor / Franco Maria Nardini ; Nadia Pisanti ; Rossano Venturini. Springer Science and Business Media Deutschland GmbH, 2023. pp. 14-27 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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author = "Amihood Amir and Eitan Kondratovsky and Avivit Levy",

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Amir, A, Kondratovsky, E & Levy, A 2023, On Suffix Tree Detection. in FM Nardini, N Pisanti & R Venturini (eds), String Processing and Information Retrieval - 30th International Symposium, SPIRE 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14240 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 14-27, 30th International Symposium on String Processing and Information Retrieval, SPIRE 2023, Pisa, Italy, 26/09/23. https://doi.org/10.1007/978-3-031-43980-3_2

On Suffix Tree Detection. / Amir, Amihood; Kondratovsky, Eitan; Levy, Avivit.
String Processing and Information Retrieval - 30th International Symposium, SPIRE 2023, Proceedings. ed. / Franco Maria Nardini; Nadia Pisanti; Rossano Venturini. Springer Science and Business Media Deutschland GmbH, 2023. p. 14-27 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14240 LNCS).

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

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AU - Levy, Avivit

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Amir A, Kondratovsky E, Levy A. On Suffix Tree Detection. In Nardini FM, Pisanti N, Venturini R, editors, String Processing and Information Retrieval - 30th International Symposium, SPIRE 2023, Proceedings. Springer Science and Business Media Deutschland GmbH. 2023. p. 14-27. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-43980-3_2

On Suffix Tree Detection

Abstract

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Keywords

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