## Abstract

String matching is rich with a variety of algorithmic tools. In contrast, multidimensional matching has a rather sparse set of techniques. This paper presents a new algorithmic technique for two-dimensional matching, that of periodicity analysis. Periodicity in strings has been used to solve string matching problems. The success of these algorithms suggests that periodicity can be as important a tool in multidimensional matching. However, multidimensional periodicity is not as simple as it is in strings and was not formally studied or used in pattern matching. This paper's main contribution is defining and analysing two-dimensional periodicity in rectangular arrays. In addition, we introduce a new pattern matching paradigm - Compressed Matching. A text array T and a pattern array P are given in compressed forms c(T) and c(P). We seek all appearances of P in T, without decompressing T. By using periodicity analysis, we show that for the two-dimensional run-length compression there is a O(|c(T)| log |P| + |P|), or almost optimal algorithm that can achieve a search time that is sublinear in the size of the text |T|.

Original language | English |
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Title of host publication | Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 |

Publisher | Association for Computing Machinery |

Pages | 440-452 |

Number of pages | 13 |

ISBN (Electronic) | 089791466X |

State | Published - 1 Sep 1992 |

Externally published | Yes |

Event | 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 - Orlando, United States Duration: 27 Jan 1992 → 29 Jan 1992 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | Part F129721 |

### Conference

Conference | 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 |
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Country/Territory | United States |

City | Orlando |

Period | 27/01/92 → 29/01/92 |

### Bibliographical note

Funding Information:String periodicity is an intuitively clear concept and the properties of a string period are simple and well understood. Two-dimensional periodicit,y, though, presents some difficulties. Periodicity in the pJane is easy to de- fine. However, we are seeking the period of a finite rectangle. The concept of a “smallest” period that defines _Y%Hege of Computing, Georgia I&tit ute of Technology. tially supported by NSF grant IRI-901 305.5. t Department, of Computer Science, University

### Funding

String periodicity is an intuitively clear concept and the properties of a string period are simple and well understood. Two-dimensional periodicit,y, though, presents some difficulties. Periodicity in the pJane is easy to de- fine. However, we are seeking the period of a finite rectangle. The concept of a “smallest” period that defines _Y%Hege of Computing, Georgia I&tit ute of Technology. tially supported by NSF grant IRI-901 305.5. t Department, of Computer Science, University

Funders | Funder number |
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National Science Foundation | IRI-901 305.5 |