### 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 |
---|---|

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

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

Volume | 92 |

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 |

### Other

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

Country | Thailand |

City | Phuket |

Period | 12/9/17 → 12/22/17 |

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

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

**Almost linear time computation of maximal repetitions in run length encoded strings.** / Fujishige, Yuta; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*28th International Symposium on Algorithms and Computation, ISAAC 2017.*vol. 92, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 28th International Symposium on Algorithms and Computation, ISAAC 2017, Phuket, Thailand, 12/9/17. https://doi.org/10.4230/LIPIcs.ISAAC.2017.33

}

TY - GEN

T1 - Almost linear time computation of maximal repetitions in run length encoded strings

AU - Fujishige, Yuta

AU - Nakashima, Yuto

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85038564653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038564653&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2017.33

DO - 10.4230/LIPIcs.ISAAC.2017.33

M3 - Conference contribution

VL - 92

BT - 28th International Symposium on Algorithms and Computation, ISAAC 2017

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -