### Abstract

Lempel-Ziv 1977 (LZ77) parsing, matching statistics and the Burrows-Wheeler Transform (BWT) are all fundamental elements of stringology. In a series of recent papers, Policriti and Prezza (DCC 2016 and Algorithmica, CPM 2017) showed how we can use an augmented run-length compressed BWT (RLBWT) of the reverse T^{R} of a text T, to compute offline the LZ77 parse of T in O(n log r) time and O(r) space, where n is the length of T and r is the number of runs in the BWT of T^{R}. In this paper we first extend a well-known technique for updating an unaugmented RLBWT when a character is prepended to a text, to work with Policriti and Prezza's augmented RLBWT. This immediately implies that we can build online the LZ77 parse of T while still using O(n log r) time and O(r) space; it also seems likely to be of independent interest. Our experiments, using an extension of Ohno, Takabatake, I and Sakamoto's (IWOCA 2017) implementation of updating, show our approach is both time- and space-efficient for repetitive strings. We then show how to augment the RLBWT further -albeit making it static again and increasing its space by a factor proportional to the size of the alphabet -such that later, given another string S and O(log log n)-time random access to T, we can compute the matching statistics of S with respect to T in O(|S| log log n) time.

Original language | English |
---|---|

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 | 71-712 |

Number of pages | 642 |

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 |
---|---|

Volume | 105 |

ISSN (Print) | 1868-8969 |

### Other

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

Country | China |

City | Qingdao |

Period | 7/2/18 → 7/4/18 |

### All Science Journal Classification (ASJC) codes

- Software

## Fingerprint Dive into the research topics of 'Online LZ77 parsing and matching statistics with RLBWTs'. Together they form a unique fingerprint.

## Cite this

*29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018*(pp. 71-712). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 105). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CPM.2018.7