### Abstract

We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in O(N logN) time and uses only O(N log σ) bits of working space, where N is the length of the string and σ is the size of the alphabet. This is a notable improvement compared to the performance of previous on-line algorithms using the same order of working space but running in either O(N log^{3}N) time (Okanohara & Sadakane 2009) or O(N log^{2}N) time (Starikovskaya 2012). The key to our new algorithm is in the utilization of an elegant but less popular index structure called Directed Acyclic Word Graphs, or DAWGs (Blumer et al. 1985). We also present an opportunistic variant of our algorithm, which, given the run length encoding of size m of a string of length N, computes the Lempel-Ziv factorization of the string on-line, in O (m · min{n (log logm)(log logN)/log log logN , √ logm/log logm o})time and O(mlogN) bits of space.

Original language | English |
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Title of host publication | 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 |

Editors | Natacha Portier, Ernst W. Mayr |

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

Pages | 675-686 |

Number of pages | 12 |

ISBN (Electronic) | 9783939897651 |

DOIs | |

Publication status | Published - Mar 1 2014 |

Event | 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 - Lyon, France Duration: Mar 5 2014 → Mar 8 2014 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 25 |

ISSN (Print) | 1868-8969 |

### Other

Other | 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 |
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Country | France |

City | Lyon |

Period | 3/5/14 → 3/8/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014*(pp. 675-686). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 25). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.STACS.2014.675