### Abstract

We revisit the problem of computing the Lyndon factorization of a string w of length N which is given as a straight line program (SLP) of size n. For this problem, we show a new algorithm which runs in O(P(n,N) + Q(n,N)n log logN) time and O(n logN + S(n,N)) space where P(n,N), S(n,N), Q(n,N) are respectively the pre-processing time, space, and query time of a data structure for longest common extensions (LCE) on SLPs. Our algorithm improves the algorithm proposed by I et al. (TCS '17), and can be more efficient than the O(N)-time solution by Duval (J. Algorithms '83) when w is highly compressible.

Original language | English |
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Title of host publication | 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 |

Editors | Binhai Zhu, Gonzalo Navarro, David Sankoff |

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

Pages | 241-2410 |

Number of pages | 2170 |

ISBN (Electronic) | 9783959770743 |

DOIs | |

Publication status | Published - May 1 2018 |

Event | 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 - Qingdao, China Duration: Jul 2 2018 → Jul 4 2018 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 105 |

ISSN (Print) | 1868-8969 |

### Other

Other | 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 |
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Country | China |

City | Qingdao |

Period | 7/2/18 → 7/4/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018*(pp. 241-2410). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 105). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CPM.2018.24

**Lyndon factorization of grammar compressed texts revisited.** / Furuya, Isamu; Nakashima, Yuto; I, Tomohiro; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018.*Leibniz International Proceedings in Informatics, LIPIcs, vol. 105, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 241-2410, 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018, Qingdao, China, 7/2/18. https://doi.org/10.4230/LIPIcs.CPM.2018.24

}

TY - GEN

T1 - Lyndon factorization of grammar compressed texts revisited

AU - Furuya, Isamu

AU - Nakashima, Yuto

AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2018/5/1

Y1 - 2018/5/1

N2 - We revisit the problem of computing the Lyndon factorization of a string w of length N which is given as a straight line program (SLP) of size n. For this problem, we show a new algorithm which runs in O(P(n,N) + Q(n,N)n log logN) time and O(n logN + S(n,N)) space where P(n,N), S(n,N), Q(n,N) are respectively the pre-processing time, space, and query time of a data structure for longest common extensions (LCE) on SLPs. Our algorithm improves the algorithm proposed by I et al. (TCS '17), and can be more efficient than the O(N)-time solution by Duval (J. Algorithms '83) when w is highly compressible.

AB - We revisit the problem of computing the Lyndon factorization of a string w of length N which is given as a straight line program (SLP) of size n. For this problem, we show a new algorithm which runs in O(P(n,N) + Q(n,N)n log logN) time and O(n logN + S(n,N)) space where P(n,N), S(n,N), Q(n,N) are respectively the pre-processing time, space, and query time of a data structure for longest common extensions (LCE) on SLPs. Our algorithm improves the algorithm proposed by I et al. (TCS '17), and can be more efficient than the O(N)-time solution by Duval (J. Algorithms '83) when w is highly compressible.

UR - http://www.scopus.com/inward/record.url?scp=85048271134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048271134&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.CPM.2018.24

DO - 10.4230/LIPIcs.CPM.2018.24

M3 - Conference contribution

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 241

EP - 2410

BT - 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018

A2 - Zhu, Binhai

A2 - Navarro, Gonzalo

A2 - Sankoff, David

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

ER -