Two-dimensional pattern matching with rotations

Amihood Amir; Ayelet Butman; Maxime Crochemore; Gad M. Landau; Mary Schaps

doi:10.1016/j.tcs.2003.10.039

Two-dimensional pattern matching with rotations

Amihood Amir, Ayelet Butman, Maxime Crochemore, Gad M. Landau, Mary Schaps

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

The problem of pattern matching with rotation is that of finding all occurrences of a two-dimensional pattern in a text, in all possible rotations. We prove an upper and lower bound on the number of such different possible rotated patterns. Subsequently, given an m×m array (pattern) and an n×n array (text) over some finite alphabet Σ, we present a new method yielding an O(n²m³) time algorithm for this problem.

Original language	English
Pages (from-to)	173-187
Number of pages	15
Journal	Theoretical Computer Science
Volume	314
Issue number	1-2
DOIs	https://doi.org/10.1016/j.tcs.2003.10.039
State	Published - 25 Feb 2004

Bibliographical note

Funding Information:
Part of this research was conducted while the 2rst and fourth authors were visiting the University of Marne-La-Vall;ee supported by Arc-en-Ciel/Keshet, French–Israeli Scienti2c and Technical Cooperation Program. ∗Corresponding author. E-mail addresses: [email protected] (A. Amir), [email protected] (A. Butman), [email protected] (G. M. Landau), [email protected] (M. Schaps). 1Partially supported by NSF grant CCR-01-04494, ISF grant 282/01, and an Israel–France exchange scientist grant funded by the Israel Ministry of Science. 2Partially supported by CNRS, NATO Science Programme grant PST.CLG.977017, and by Arc-en-Ciel/Keshet, French–Israeli Scienti2c and Technical Cooperation Program. 3Partially supported by NSF grants CCR-9610238 and CCR-0104307, by NATO Science Programme grant PST.CLG.977017, by the Israel Science Foundation grants 173/98 and 282/01, by the FIRST Foundation of the Israel Academy of Science and Humanities, by IBM Faculty Partnership Award, and by Arc-en-Ciel/Keshet, French–Israeli Scienti2c and Technical Cooperation Program.

Funding

Part of this research was conducted while the 2rst and fourth authors were visiting the University of Marne-La-Vall;ee supported by Arc-en-Ciel/Keshet, French–Israeli Scienti2c and Technical Cooperation Program. ∗Corresponding author. E-mail addresses: [email protected] (A. Amir), [email protected] (A. Butman), [email protected] (G. M. Landau), [email protected] (M. Schaps). 1Partially supported by NSF grant CCR-01-04494, ISF grant 282/01, and an Israel–France exchange scientist grant funded by the Israel Ministry of Science. 2Partially supported by CNRS, NATO Science Programme grant PST.CLG.977017, and by Arc-en-Ciel/Keshet, French–Israeli Scienti2c and Technical Cooperation Program. 3Partially supported by NSF grants CCR-9610238 and CCR-0104307, by NATO Science Programme grant PST.CLG.977017, by the Israel Science Foundation grants 173/98 and 282/01, by the FIRST Foundation of the Israel Academy of Science and Humanities, by IBM Faculty Partnership Award, and by Arc-en-Ciel/Keshet, French–Israeli Scienti2c and Technical Cooperation Program.

Funders	Funder number
FIRST Foundation of the Israel Academy of Science and Humanities
French–Israeli Scienti2c and Technical Cooperation Program
National Science Foundation	CCR-01-04494
International Business Machines Corporation
North Atlantic Treaty Organization	CCR-0104307, CCR-9610238, PST.CLG.977017
Israel Science Foundation	282/01, 173/98
Centre National de la Recherche Scientifique
Ministry of science and technology, Israel

Keywords

Design and analysis of algorithms
Rotation
Two-dimensional pattern matching

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10.1016/j.tcs.2003.10.039

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abstract = "The problem of pattern matching with rotation is that of finding all occurrences of a two-dimensional pattern in a text, in all possible rotations. We prove an upper and lower bound on the number of such different possible rotated patterns. Subsequently, given an m×m array (pattern) and an n×n array (text) over some finite alphabet Σ, we present a new method yielding an O(n2m3) time algorithm for this problem.",

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Two-dimensional pattern matching with rotations

Abstract

Bibliographical note

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Keywords

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