## Abstract

Recent proliferation of digitized data and the unprecedented growth in the volume of stored and transmitted data motivated the definition of the compressed matching paradigm. This is the problem of efficiently finding a pattern P in a compressed text T without the need to decompress. We present the first optimal two-dimensional compressed matching algorithm. The compression under consideration is the two dimensional run-length compression, used by FAX transmission. We achieve optimal time by proving new properties of two-dimensional periodicity. This enables performing duels in which no witness is required. At the heart of the dueling idea lies the concept that two overlapping occurrences of a pattern in a text can use the content of a predetermined text position or witness in the overlap to eliminate one of them. Finding witnesses is a costly operation in a compressed text, thus the importance of witness-free dueling.

Original language | English |
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Pages (from-to) | 354-379 |

Number of pages | 26 |

Journal | Journal of Algorithms |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1997 |

Externally published | Yes |

### Bibliographical note

Funding Information:Recent proliferation of digitized data and the unprecedented growth in the volume of stored and transmitted data motivated the definition of the compressed matching paradigm. This is the problem of efficiently finding a pattern P in a compressed text T without the need to decompress. We present the first optimal two-dimensional compressed matching algorithm. The compression under consideration is the two dimensional run-length compression, used by FAX transmission. We achieve optimal time by proving new properties of two-dimensional periodicity. This enables performing duels in which no witness is required. At the heart of the dueling idea lies the concept that two overlapping occurrences of a pattern in a text can use the content of a predetermined text position or witness in the overlap to eliminate one of them. Finding witnesses is a costly operation in a compressed text, thus the importance of witness-free dueling. Q 1997 Academic Press UPartially supported by NSF Grant IRI-90-13055. E-mail: amir@cc.gatech.edu. ²Partially supported by NSF Grant DMS-90-05833. E-mail: benson@ecology.biomath. mssm.edu. ³Supported by DIMACS under NSF Contract STC-88-09648. E-mail: farach@cs.rutgers.edu.