## Abstract

We consider the problem of decompressing the Lempel-Ziv 77 representation of a string S of length n using a working space as close as possible to the size z of the input. The folklore solution for the problem runs in O(n) time but requires random access to the whole decompressed text. Another folklore solution is to convert LZ77 into a grammar of size O(z log(n/z)) and then stream S in linear time. In this paper, we show that O(n) time and O(z) working space can be achieved for constant-size alphabets. On general alphabets of size σ, we describe (i) a trade-off achieving O(n log^δ σ) time and O(z log^1-δ σ) space for any 0≤ δ≤ 1, and (ii) a solution achieving O(n) time and O(z log log (n/z)) space. The latter solution, in particular, dominates both folklore algorithms for the problem. Our solutions can, more generally, extract any specified subsequence of S with little overheads on top of the linear running time and working space. As an immediate corollary, we show that our techniques yield improved results for pattern matching problems on LZ77-compressed text.

Original language | English |
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Title of host publication | Proceedings of Data Compression Conference 2020 |

Editors | Ali Bilgin, Michael W. Marcellin, Joan Serra-Sagrista, James A. Storer |

Publisher | IEEE |

Publication date | Mar 2020 |

Pages | 143-152 |

Article number | 9105689 |

ISBN (Electronic) | 9781728164571 |

DOIs | |

Publication status | Published - Mar 2020 |

Event | 2020 Data Compression Conference, DCC 2020 - Snowbird, United States Duration: 24 Mar 2020 → 27 Mar 2020 |

### Conference

Conference | 2020 Data Compression Conference, DCC 2020 |
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Country/Territory | United States |

City | Snowbird |

Period | 24/03/2020 → 27/03/2020 |

Sponsor | Brandeis University, Microsoft USA, University of Arizona |