### Abstract

For α ≥ 1, an α-gapped repeat in a word w is a factor uvu of w such that |uv| ≤ α|u|; the two occurrences of a factor u in such a repeat are called arms. Such a repeat is called maximal if its arms cannot be extended simultaneously with the same symbol to the right nor to the left. We show that the number of all maximal α-gapped repeats occurring in words of length n is upper bounded by 18αn, allowing us to construct an algorithm finding all maximal α-gapped repeats of a word on an integer alphabet of size n^{O(1)}; in O(αn) time. This result is optimal as there are words that have Θ(αn) maximal α-gapped repeats. Our techniques can be extended to get comparable results in the case of α-gapped palindromes, i.e., factors uvu^{T} with |uv| ≤ α|u|.

Original language | English |
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Title of host publication | 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016 |

Editors | Heribert Vollmer, Nicolas Ollinger |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770019 |

DOIs | |

Publication status | Published - Feb 1 2016 |

Event | 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016 - Orleans, France Duration: Feb 17 2016 → Feb 20 2016 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 47 |

ISSN (Print) | 1868-8969 |

### Other

Other | 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016 |
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Country | France |

City | Orleans |

Period | 2/17/16 → 2/20/16 |

### All Science Journal Classification (ASJC) codes

- Software

## Cite this

*33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016*[39] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 47). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.STACS.2016.39