Efficient pattern matching with scaling

Amihood Amir; Gad M. Landau; Uzi Vishkin

Efficient pattern matching with scaling

Amihood Amir, Gad M. Landau, Uzi Vishkin

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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
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

Conference

Conference	1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990
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
General Mathematics

Cite this

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title = "Efficient pattern matching with scaling",

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.",

author = "Amihood Amir and Landau, {Gad M.} and Uzi Vishkin",

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.; 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990 ; Conference date: 22-01-1990 Through 24-01-1990",

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series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

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Amir, A, Landau, GM & Vishkin, U 1990, Efficient pattern matching with scaling. in Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, pp. 344-357, 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990, San Francisco, United States, 22/01/90.

Efficient pattern matching with scaling. / Amir, Amihood; Landau, Gad M.; Vishkin, Uzi.
Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990. Association for Computing Machinery, 1990. p. 344-357 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - 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.

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N2 - 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.

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M3 - Conference contribution

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T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

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BT - Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990

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ER -

Efficient pattern matching with scaling

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

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Cite this