## Abstract

Given a string S over a finite alphabet Σ, the character set (also called the fingerprint) of a substring S^{′} of S is the subset C ⊆ Σ of the symbols occurring in S^{′}. The study of the character sets of all the substrings of a given string (or a given collection of strings) appears in several domains such as rule induction for natural language processing or comparative genomics. Several computational problems concerning the character sets of a string arise from these applications, especially: (1)Output all the maximal locations of substrings having a given character set.(2)Output for each character set C occurring in a given string (or a given collection of strings) all the maximal locations of C. Denoting by n the total length of the considered string or collection of strings, we solve the first problem in Θ (n) time using Θ (n) space. We present two algorithms solving the second problem. The first one runs in Θ (n^{2}) time using Θ (n) space. The second algorithm has Θ (n | Σ | log | Σ |) time and Θ (n) space complexity and is an adaptation of an algorithm by Amir et al. [A. Amir, A. Apostolico, G.M. Landau, G. Satta, Efficient text fingerprinting via Parikh mapping, J. Discrete Algorithms 26 (2003) 1-13].

Original language | English |
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Pages (from-to) | 330-340 |

Number of pages | 11 |

Journal | Journal of Discrete Algorithms |

Volume | 5 |

Issue number | 2 SPEC. ISS. |

DOIs | |

State | Published - 1 Jan 2007 |

## Keywords

- Character sets
- Combinatorial algorithms on words
- Comparative genomics
- Fingerprints
- Natural language processing

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics