### Abstract

We consider efficiency of NC-algorithms for pattern-searching in highly compressed one- and two-dimensional texts. “Highly compressed” means that the text can be exponentially large with respect to its compressed version, and “fast” means “in polylogarithmic time”. Given an uncompressed pattern P and a compressed version of a text T, the compressed matching problem is to test if P occurs in T. Two types of closely related compressed representations of 1-dimensional texts are considered: the Lempel-Ziv encodings (LZ, in short) and restricted LZ encodings (RLZ, in short). For highly compressed texts there is a small difference between them, in extreme situations both of them compress text exponentially, e.g. Fibonacci words of size N have compressed versions of size O(logN) for LZ and Restricted LZ encodings. Despite similarities we prove that LZ-compressed matching is P-complete while RLZ-compressed matching is rather trivially in NC. We show how to improve a naive straightforward NC algorithm and obtain almost optimal parallel RLZ-compressed matching applying tree-contraction techniques to directed acyclic graphs with polynomial tree-size. As a corollary we obtain an almost optimal parallel algorithm for LZW-compressed matching which is simpler than the (more general) algorithm in [11]. Highly compressed 2-dimensional texts are also considered.

Original language | English (US) |
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Title of host publication | Mathematical Foundations of Computer Science 1999 - 24th International Symposium, MFCS 1999, Proceedings |

Editors | Mirosław kutyłowski, Leszek Pacholski, Tomasz Wierzbicki |

Publisher | Springer Verlag |

Pages | 48-58 |

Number of pages | 11 |

ISBN (Print) | 3540664084, 9783540664086 |

DOIs | |

State | Published - Jan 1 1999 |

Externally published | Yes |

Event | 24th International Symposium on Mathematical Foundations of Computer Science, MFCS 1999 - Szklarska Poreba, Poland Duration: Sep 6 1999 → Sep 10 1999 |

### 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 | 1672 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 24th International Symposium on Mathematical Foundations of Computer Science, MFCS 1999 |
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Country | Poland |

City | Szklarska Poreba |

Period | 9/6/99 → 9/10/99 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Mathematical Foundations of Computer Science 1999 - 24th International Symposium, MFCS 1999, Proceedings*(pp. 48-58). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1672). Springer Verlag. https://doi.org/10.1007/3-540-48340-3_5