### Abstract

We consider the problem of computing all maximal repetitions contained in a string that is given in run-length encoding. Given a run-length encoding of a string, we show that the maximum number of maximal repetitions contained in the string is at most m+k-1, where m is the size of the run-length encoding, and k is the number of run-length factors whose exponent is at least 2. We also show an algorithm for computing all maximal repetitions in O(m α (m)) time and O(m) space, where α denotes the inverse Ackermann function.

Original language | English |
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Title of host publication | 28th International Symposium on Algorithms and Computation, ISAAC 2017 |

Editors | Takeshi Tokuyama, Yoshio Okamoto |

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

ISBN (Electronic) | 9783959770545 |

DOIs | |

Publication status | Published - Dec 1 2017 |

Event | 28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand Duration: Dec 9 2017 → Dec 22 2017 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 92 |

ISSN (Print) | 1868-8969 |

### Other

Other | 28th International Symposium on Algorithms and Computation, ISAAC 2017 |
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Country | Thailand |

City | Phuket |

Period | 12/9/17 → 12/22/17 |

### All Science Journal Classification (ASJC) codes

- Software

## Cite this

Fujishige, Y., Nakashima, Y., Inenaga, S., Bannai, H., & Takeda, M. (2017). Almost linear time computation of maximal repetitions in run length encoded strings. In T. Tokuyama, & Y. Okamoto (Eds.),

*28th International Symposium on Algorithms and Computation, ISAAC 2017*(Leibniz International Proceedings in Informatics, LIPIcs; Vol. 92). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2017.33