### Abstract

Denote by LZ(w) the coded form of a string w produced by Lempel-Ziv encoding algorithm. We consider several classical algorithmic problems for texts in the compressed setting. The first of them is the equality-testing: given LZ(w) and integers i,j,k test the equality: w[i…i+ k] = w[j… j + k]. We give a simple and efficient randomized algorithm for this problem using the finger-printing idea. The equality testing is reduced to the equivalence of certain context-free grammars generating single strings. The equality-testing is the bottleneck in other algorithms for compressed texts. We relate the time complexity of several classical problems for texts to the complexity Eq(n) of equality-testing. Assume n = |LZ(T)|, m = |LZ(P)| and U = |T|. Then we can compute the compressed representations of the sets of occurrences of P in T, periods of T, palindromes of T, and squares of T respectively in times O(n log^{2} U · Eq(m) + n^{2} log U), O(n log^{2} U · Eq(n) + n^{2} log U), O(n log^{2} U ·Eq(n) + n^{2} log U) and O(n^{2} log^{3} U · Eq(n) + n^{3} log^{2} U), where Eq(n) = O(n log log n). The randomization improves considerably upon the known deterministic algorithms.

Original language | English (US) |
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Title of host publication | Combinatorial Pattern Matching - 7th Annual Symposium, CPM 1996, Proceedings |

Editors | Gene Myers, Dan Hirschberg |

Publisher | Springer Verlag |

Pages | 39-49 |

Number of pages | 11 |

ISBN (Print) | 3540612580, 9783540612582 |

DOIs | |

State | Published - Jan 1 1996 |

Externally published | Yes |

Event | 7th Annual Symposium on Combinatorial Pattern Matching, CPM 1996 - Laguna Beach, United States Duration: Jun 10 1996 → Jun 12 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1075 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 7th Annual Symposium on Combinatorial Pattern Matching, CPM 1996 |
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Country | United States |

City | Laguna Beach |

Period | 6/10/96 → 6/12/96 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Combinatorial Pattern Matching - 7th Annual Symposium, CPM 1996, Proceedings*(pp. 39-49). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1075). Springer Verlag. https://doi.org/10.1007/3-540-61258-0_3