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On Suffix Tree Detection

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String Processing and Information Retrieval (SPIRE 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14240))

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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.

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

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Notes

  1. 1.

    Though Sect. 3 studies periodic string having period length at least 2, which we call non-trivial periodic strings, this complexity is also valid for detection of trivial periodic strings (i.e., unary strings), as follows from condition 2 of Theorem 2 in Sect. 4.

  2. 2.

    Assuming the basic terms: rooted trees, internal tree nodes and tree leaves are known.

  3. 3.

    Note that the structure of a unary string, which is a trivial periodic string with period length 1, is characterized by Theorem 2.2 in Sect. 4.

  4. 4.

    p is unique by condition 2 of Theorem 1.

  5. 5.

    The characters \(\sigma \in \varSigma \) are chosen to the edges of T’s root from left to right according to the order of \(\varSigma \), where the first edge is \(\$\).

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Author information

Authors and Affiliations

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

    Amihood Amir

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

    Eitan Kondratovsky

  3. Software Engineering Department, Shenkar College of Engineering and Design, Ramat-Gan, Israel

    Avivit Levy

Authors
  1. Amihood Amir
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  2. Eitan Kondratovsky
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  3. Avivit Levy
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Correspondence to Avivit Levy .

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Editors and Affiliations

  1. ISTI-CNR, Pisa, Italy

    Franco Maria Nardini

  2. University of Pisa, Pisa, Italy

    Nadia Pisanti

  3. University of Pisa, Pisa, Italy

    Rossano Venturini

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Amir, A., Kondratovsky, E., Levy, A. (2023). On Suffix Tree Detection. In: Nardini, F.M., Pisanti, N., Venturini, R. (eds) String Processing and Information Retrieval. SPIRE 2023. Lecture Notes in Computer Science, vol 14240. Springer, Cham. https://doi.org/10.1007/978-3-031-43980-3_2

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  • DOI: https://doi.org/10.1007/978-3-031-43980-3_2

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