### Abstract

A string x = uvu with both u, v being non-empty is called a gapped repeat with period p = |uv|, and is denoted by pair (x, p). If p ≤ α(|x| − p) with α > 1, then (x, p) is called an α-gapped repeat. An occurrence [i, i+|x|−1] of an α-gapped repeat (x, p) in a string w is called a maximal α-gapped repeat of w, if it cannot be extended either to the left or to the right in w with the same period p. Kolpakov et al. (CPM 2014) showed that, given a string of length n over a constant alphabet, all the occurrences of maximal α-gapped repeats in the string can be computed in O(α^{2}n+occ) time, where occ is the number of occurrences. In this paper, we propose a faster O(αn + occ)-time algorithm to solve this problem, improving the result of Kolpakov et al. by a factor of α.

Original language | English |
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Title of host publication | String Processing and Information Retrieval - 22nd International Symposium, SPIRE 2015, Proceedings |

Editors | Simon J. Puglisi, Costas S. Iliopoulos, Emine Yilmaz |

Publisher | Springer Verlag |

Pages | 124-136 |

Number of pages | 13 |

ISBN (Print) | 9783319238258 |

DOIs | |

Publication status | Published - Jan 1 2015 |

Event | 22nd International Symposium on String Processing and Information Retrieval, SPIRE 2015 - London, United Kingdom Duration: Sep 1 2015 → Sep 4 2015 |

### 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 | 9309 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 22nd International Symposium on String Processing and Information Retrieval, SPIRE 2015 |
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Country | United Kingdom |

City | London |

Period | 9/1/15 → 9/4/15 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*String Processing and Information Retrieval - 22nd International Symposium, SPIRE 2015, Proceedings*(pp. 124-136). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9309). Springer Verlag. https://doi.org/10.1007/978-3-319-23826-5_13

**A faster algorithm for computing maximal α-gapped repeats in a string.** / Tanimura, Yuka; Fujishige, Yuta; Tomohiro, I.; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*String Processing and Information Retrieval - 22nd International Symposium, SPIRE 2015, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9309, Springer Verlag, pp. 124-136, 22nd International Symposium on String Processing and Information Retrieval, SPIRE 2015, London, United Kingdom, 9/1/15. https://doi.org/10.1007/978-3-319-23826-5_13

}

TY - GEN

T1 - A faster algorithm for computing maximal α-gapped repeats in a string

AU - Tanimura, Yuka

AU - Fujishige, Yuta

AU - Tomohiro, I.

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2015/1/1

Y1 - 2015/1/1

N2 - A string x = uvu with both u, v being non-empty is called a gapped repeat with period p = |uv|, and is denoted by pair (x, p). If p ≤ α(|x| − p) with α > 1, then (x, p) is called an α-gapped repeat. An occurrence [i, i+|x|−1] of an α-gapped repeat (x, p) in a string w is called a maximal α-gapped repeat of w, if it cannot be extended either to the left or to the right in w with the same period p. Kolpakov et al. (CPM 2014) showed that, given a string of length n over a constant alphabet, all the occurrences of maximal α-gapped repeats in the string can be computed in O(α2n+occ) time, where occ is the number of occurrences. In this paper, we propose a faster O(αn + occ)-time algorithm to solve this problem, improving the result of Kolpakov et al. by a factor of α.

AB - A string x = uvu with both u, v being non-empty is called a gapped repeat with period p = |uv|, and is denoted by pair (x, p). If p ≤ α(|x| − p) with α > 1, then (x, p) is called an α-gapped repeat. An occurrence [i, i+|x|−1] of an α-gapped repeat (x, p) in a string w is called a maximal α-gapped repeat of w, if it cannot be extended either to the left or to the right in w with the same period p. Kolpakov et al. (CPM 2014) showed that, given a string of length n over a constant alphabet, all the occurrences of maximal α-gapped repeats in the string can be computed in O(α2n+occ) time, where occ is the number of occurrences. In this paper, we propose a faster O(αn + occ)-time algorithm to solve this problem, improving the result of Kolpakov et al. by a factor of α.

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U2 - 10.1007/978-3-319-23826-5_13

DO - 10.1007/978-3-319-23826-5_13

M3 - Conference contribution

SN - 9783319238258

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 124

EP - 136

BT - String Processing and Information Retrieval - 22nd International Symposium, SPIRE 2015, Proceedings

A2 - Puglisi, Simon J.

A2 - Iliopoulos, Costas S.

A2 - Yilmaz, Emine

PB - Springer Verlag

ER -