## Abstract

The problem of pattern matching with scalingis defined. The input for the two-dimensional version of the problem consists of an n×n "text" matrix and an m×m "pattern" matrix. We want to find all occurrences of the pattern in the text, scaled to all natural multiples. That is, for every natural number i, 1 ≤ i ≤ 〈n/m〉 we seek all occurrences of the pattern in the text, where each character of the pattern corresponds to an i×i square in the text. This problem is useful for some tasks in computer vision. Our main contribution is a linear time algorithm for the problem. We also consider situations where the text is provided in a less redundant form. For instance, suppose that a repeating character is compressed into one character, along with the number of repetitions. We show how to enhance our algorithm so that its running time may become sublinear with respect to the original redundant input representation. Our algorithms are based on a new algorithmic approach to two dimensional string matching. Unlike existing approaches, the new approach does not work by reducing a two dimensional problem into an one dimensional problem.

Original language | English |
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Title of host publication | Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990 |

Publisher | Association for Computing Machinery |

Pages | 344-357 |

Number of pages | 14 |

ISBN (Electronic) | 0898712513 |

State | Published - 1 Jan 1990 |

Externally published | Yes |

Event | 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990 - San Francisco, United States Duration: 22 Jan 1990 → 24 Jan 1990 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Conference

Conference | 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990 |
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Country/Territory | United States |

City | San Francisco |

Period | 22/01/90 → 24/01/90 |

### Bibliographical note

Funding Information:*University of Maryland, College Park, Maryland. Partially supported by NSF grant CCR-8803641 and a University of Maryland Full Year Research Award. t Polytechnic University, Brooklyn, NY. Partially supported by NSF grant CCR8908286 and the New York State Science and Technology Foundation, Center for Advanced Technology Foundation, Center for Advanced Technology in Telecommnni-cations, Polytechnic University, Brooklyn, NY. 2 University of Maryland and Tel Aviv University. Partially supported by NSF grants CCR-8615337 and CCR-8906949 and ONR grant N 00014-85-K-0046.

Funding Information:

Partially supported by NSF grant CCR-8803641 and a University of Maryland Full Year Research Award.

## ASJC Scopus subject areas

- Software
- Mathematics (all)