### Abstract

Kolpakov and Kucherov proposed a variant of the Lempel-Ziv factorization, called the reversed Lempel-Ziv (RLZ) factorization (Theoretical Computer Science, 410(51):5365-5373, 2009). In this paper, we present an on-line algorithm that computes the RLZ factorization of a given string w of length n in 0(n log^{2} n) time using 0(n log σ) bits of space, where a < n is the alphabet size. Also, we introduce a new variant of the RLZ factorization with self-references, and present two on-line algorithms to compute this variant, in 0(n log σ) time using 0(n log n) bits of space, and in 0(n log^{2} n) time using 0(n log σ) bits of space.

Original language | English |
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Title of host publication | Proceedings of the Prague Stringology Conference 2013, PSC 2013 |

Publisher | Prague Stringology Club |

Pages | 107-118 |

Number of pages | 12 |

ISBN (Print) | 9788001053300 |

Publication status | Published - Jan 1 2013 |

Event | Prague Stringology Conference 2013, PSC 2013 - Prague, Czech Republic Duration: Sep 2 2013 → Sep 4 2013 |

### Publication series

Name | Proceedings of the Prague Stringology Conference 2013, PSC 2013 |
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### Other

Other | Prague Stringology Conference 2013, PSC 2013 |
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Country | Czech Republic |

City | Prague |

Period | 9/2/13 → 9/4/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Proceedings of the Prague Stringology Conference 2013, PSC 2013*(pp. 107-118). (Proceedings of the Prague Stringology Conference 2013, PSC 2013). Prague Stringology Club.

**Computing reversed Lempel-Ziv factorization online.** / Sugimoto, Shiho; I, Tomohiro; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*Proceedings of the Prague Stringology Conference 2013, PSC 2013.*Proceedings of the Prague Stringology Conference 2013, PSC 2013, Prague Stringology Club, pp. 107-118, Prague Stringology Conference 2013, PSC 2013, Prague, Czech Republic, 9/2/13.

}

TY - GEN

T1 - Computing reversed Lempel-Ziv factorization online

AU - Sugimoto, Shiho

AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Kolpakov and Kucherov proposed a variant of the Lempel-Ziv factorization, called the reversed Lempel-Ziv (RLZ) factorization (Theoretical Computer Science, 410(51):5365-5373, 2009). In this paper, we present an on-line algorithm that computes the RLZ factorization of a given string w of length n in 0(n log2 n) time using 0(n log σ) bits of space, where a < n is the alphabet size. Also, we introduce a new variant of the RLZ factorization with self-references, and present two on-line algorithms to compute this variant, in 0(n log σ) time using 0(n log n) bits of space, and in 0(n log2 n) time using 0(n log σ) bits of space.

AB - Kolpakov and Kucherov proposed a variant of the Lempel-Ziv factorization, called the reversed Lempel-Ziv (RLZ) factorization (Theoretical Computer Science, 410(51):5365-5373, 2009). In this paper, we present an on-line algorithm that computes the RLZ factorization of a given string w of length n in 0(n log2 n) time using 0(n log σ) bits of space, where a < n is the alphabet size. Also, we introduce a new variant of the RLZ factorization with self-references, and present two on-line algorithms to compute this variant, in 0(n log σ) time using 0(n log n) bits of space, and in 0(n log2 n) time using 0(n log σ) bits of space.

UR - http://www.scopus.com/inward/record.url?scp=84884642375&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884642375&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84884642375

SN - 9788001053300

T3 - Proceedings of the Prague Stringology Conference 2013, PSC 2013

SP - 107

EP - 118

BT - Proceedings of the Prague Stringology Conference 2013, PSC 2013

PB - Prague Stringology Club

ER -