### Abstract

We study the fully compressed pattern matching problem (FCPM problem): Given T and P which are descriptions of text T and pattern P respectively, find the occurrences of P in T without decompressing T or P. This problem is rather challenging since patterns are also given in a compressed form. In this paper we present an FCPM algorithm for simple collage systems. Collage systems are a general framework representing various kinds of dictionary-based compressions in a uniform way, and simple collage systems are a subclass that includes LZW and LZ78 compressions. Collage systems are of the form (〈D, S〉, where D is a dictionary and S is a sequence of variables from D. Our FCPM algorithm performs in O(∥D∥ ^{2} + mn log|S|) time, where n = |T| = ∥D∥ + |S| and m = |P|. This is faster than the previous best result of O(m ^{2}n ^{2}) time.

Original language | English |
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Pages (from-to) | 1155-1166 |

Number of pages | 12 |

Journal | International Journal of Foundations of Computer Science |

Volume | 16 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2005 Dec 1 |

### Keywords

- Algorithm
- Collage systems
- Fully compressed pattern matching
- String processing
- Text compression

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

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## Cite this

*International Journal of Foundations of Computer Science*,

*16*(6), 1155-1166. https://doi.org/10.1142/S0129054105003728