## 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 |
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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 | |

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) |
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Volume | 14240 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 30th International Symposium on String Processing and Information Retrieval, SPIRE 2023 |
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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 |
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United States-Israel Binational Science Foundation | 2018141 |

Israel Science Foundation | 1475/18 |

## Keywords

- Periodic string
- Reverse engineering
- Suffix tree
- Suffix tree detection