## Abstract

The rapidly growing need for analysis of digitized images in multimedia systems has led to a variety of interesting problems in multidimensional pattern matching. One of the problems is that of scaled matching, finding all appearances of a pattern in a text in all sizes. Another important problem is dictionary matching, a quick search through a dictionary of preprocessed patterns in order to find all dictionary patterns that appear in the input text. In this paper we provide a simple algorithm for two-dimensional scaled matching. Our algorithm is the first linear-time alphabet-independent scaled matching algorithm. Its running time is O(\T\), where \T\ is the text size, and is independent of |Σ|, the size of the alphabet. The main idea behind our algorithm is to identify and exploit a scaling-invariant property of patterns. Our technique generalizes to produce the first known algorithm for scaled dictionary matching. We can find all appearances of all dictionary patterns that appear in the input text in any discrete scale. The time bounds of our algorithm are equal to the currently known exact (no scaling) two-dimensional dictionary matching algorithms.

Original language | English |
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Pages (from-to) | 34-62 |

Number of pages | 29 |

Journal | Journal of Algorithms |

Volume | 36 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2000 |

### Bibliographical note

Funding Information:The rapidly growing need for analysis of digitized images in multimedia systems has led to a variety of interesting problems in multidimensional pattern matching. One of the problems is that of scaled matching, finding all appearances of a pattern in a text in all sizes. Another important problem is dictionary matching, a quick search through a dictionary of preprocessed patterns in order to find all dictionary patterns that appear in the input text. In this paper we provide a simple algorithm for two-dimensional scaled matching. Our algorithm is the first linear-time alphabet-independent scaled matching algorithm. Its running time is O(<T<), where <T< is the text size, and is independent of <Σ<, the size of the alphabet. The main idea behind our algorithm is to identify and exploit a scaling-in¨ariant property of patterns. Our technique generalizes to produce the first known algorithm for scaled dictionary matching. We can find all appearances of all dictionary patterns that appear in the input text in any discrete scale. The time bounds of our algorithm are equal to the currently known exact (no scaling) two-dimensional dictionary matching algorithms. Q 2000 Academic Press 1A preliminary version of this paper appeared in Combinatorial Pattern Matching, 1996. 2Partially supported by NSF Grant CCR-96-10170, BSF Grant 96-00509, and a BIU internal research grant.