### Abstract

In this talk, we introduce our recent data structure for longest common extension (LCE) queries on grammar-compressed strings. Our preprocessing input is a straight-line program (SLP) of size n describing a string w of length N, which is essentially a CFG in the Chomsky normal form generating only w. We can preprocess the input SLP in O(n log log n logN log N) time so that later, given two variables and two positions in the strings derived by the variables, we can answer the corresponding LCE query in O(logN log N) time. Our LCE data structure requires O(z logN log N) words of space, where z is the size of the Lempel-Ziv 77 factorization of w. We also show several applications of our LCE data structure on SLPs.

Original language | English |
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Title of host publication | Proceedings of the Prague Stringology Conference 2015, PSC 2015 |

Editors | Jan Zd'arek, Jan Holub |

Publisher | Prague Stringology Club |

Pages | 1-4 |

Number of pages | 4 |

ISBN (Electronic) | 9788001057872 |

Publication status | Published - Jan 1 2015 |

Event | 19th Prague Stringology Conference, PSC 2015 - Prague, Czech Republic Duration: Aug 24 2015 → Aug 26 2015 |

### Publication series

Name | Proceedings of the Prague Stringology Conference 2015, PSC 2015 |
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### Other

Other | 19th Prague Stringology Conference, PSC 2015 |
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Country | Czech Republic |

City | Prague |

Period | 8/24/15 → 8/26/15 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

*Proceedings of the Prague Stringology Conference 2015, PSC 2015*(pp. 1-4). (Proceedings of the Prague Stringology Conference 2015, PSC 2015). Prague Stringology Club.