### Abstract

We present a new linear time algorithm for computing the Lempel-Ziv Factorization (LZ77) of a given string of length N on an alphabet of size σ, that utilizes only Nlog N + O(σ log N) bits of working space. When the alphabet size is small, this greatly improves the previous best space requirement for linear time LZ77 factorization (Kärkkäinen et al. CPM 2013), which is 2Nlog N bits, i.e. two integer arrays of length N. Experiments show that despite the added complexity of the algorithm, the speed of the algorithm is only around two to three times slower than previous fastest linear time algorithms.

Original language | English |
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Title of host publication | Proceedings - DCC 2014 |

Subtitle of host publication | 2014 Data Compression Conference |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 163-172 |

Number of pages | 10 |

ISBN (Print) | 9781479938827 |

DOIs | |

Publication status | Published - Jan 1 2014 |

Event | 2014 Data Compression Conference, DCC 2014 - Snowbird, UT, United States Duration: Mar 26 2014 → Mar 28 2014 |

### Other

Other | 2014 Data Compression Conference, DCC 2014 |
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Country | United States |

City | Snowbird, UT |

Period | 3/26/14 → 3/28/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications

### Cite this

*Proceedings - DCC 2014: 2014 Data Compression Conference*(pp. 163-172). [6824424] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DCC.2014.62

**Space efficient linear time lempel-ziv factorization for small alphabets.** / Goto, Keisuke; Bannai, Hideo.

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

*Proceedings - DCC 2014: 2014 Data Compression Conference.*, 6824424, Institute of Electrical and Electronics Engineers Inc., pp. 163-172, 2014 Data Compression Conference, DCC 2014, Snowbird, UT, United States, 3/26/14. https://doi.org/10.1109/DCC.2014.62

}

TY - GEN

T1 - Space efficient linear time lempel-ziv factorization for small alphabets

AU - Goto, Keisuke

AU - Bannai, Hideo

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We present a new linear time algorithm for computing the Lempel-Ziv Factorization (LZ77) of a given string of length N on an alphabet of size σ, that utilizes only Nlog N + O(σ log N) bits of working space. When the alphabet size is small, this greatly improves the previous best space requirement for linear time LZ77 factorization (Kärkkäinen et al. CPM 2013), which is 2Nlog N bits, i.e. two integer arrays of length N. Experiments show that despite the added complexity of the algorithm, the speed of the algorithm is only around two to three times slower than previous fastest linear time algorithms.

AB - We present a new linear time algorithm for computing the Lempel-Ziv Factorization (LZ77) of a given string of length N on an alphabet of size σ, that utilizes only Nlog N + O(σ log N) bits of working space. When the alphabet size is small, this greatly improves the previous best space requirement for linear time LZ77 factorization (Kärkkäinen et al. CPM 2013), which is 2Nlog N bits, i.e. two integer arrays of length N. Experiments show that despite the added complexity of the algorithm, the speed of the algorithm is only around two to three times slower than previous fastest linear time algorithms.

UR - http://www.scopus.com/inward/record.url?scp=84903469508&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903469508&partnerID=8YFLogxK

U2 - 10.1109/DCC.2014.62

DO - 10.1109/DCC.2014.62

M3 - Conference contribution

AN - SCOPUS:84903469508

SN - 9781479938827

SP - 163

EP - 172

BT - Proceedings - DCC 2014

PB - Institute of Electrical and Electronics Engineers Inc.

ER -