Two-dimensional pattern matching with rotations

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

doi:10.1007/3-540-44888-8_2

Two-dimensional pattern matching with rotations

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

Georgia Institute of Technology
Bar-Ilan University
Université de Marne-la-Vallée
King's College London
University of Haifa
Polytechnic University

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

8 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 x m array (pattern) and an n x 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
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Ricardo Baeza-Yates, Edgar Chavez, Maxime Crochemore
Publisher	Springer Verlag
Pages	17-31
Number of pages	15
ISBN (Print)	3540403116, 9783540403111
DOIs	https://doi.org/10.1007/3-540-44888-8_2
State	Published - 2003

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2676
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

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
Iowa Science Foundation	282/01
Israel Science Foundation	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

Access to Document

10.1007/3-540-44888-8_2

Cite this

Amir, A., Butman, A., Crochemore, M., Landau, G. M., & Schaps, M. (2003). Two-dimensional pattern matching with rotations. In R. Baeza-Yates, E. Chavez, & M. Crochemore (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 17-31). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2676). Springer Verlag. https://doi.org/10.1007/3-540-44888-8_2

Amir, Amihood ; Butman, Ayelet ; Crochemore, Maxime et al. / Two-dimensional pattern matching with rotations. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Ricardo Baeza-Yates ; Edgar Chavez ; Maxime Crochemore. Springer Verlag, 2003. pp. 17-31 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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 x m array (pattern) and an n x 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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Amir, A, Butman, A, Crochemore, M, Landau, GM & Schaps, M 2003, Two-dimensional pattern matching with rotations. in R Baeza-Yates, E Chavez & M Crochemore (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2676, Springer Verlag, pp. 17-31. https://doi.org/10.1007/3-540-44888-8_2

Two-dimensional pattern matching with rotations. / Amir, Amihood; Butman, Ayelet; Crochemore, Maxime et al.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Ricardo Baeza-Yates; Edgar Chavez; Maxime Crochemore. Springer Verlag, 2003. p. 17-31 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2676).

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

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AU - Butman, Ayelet

AU - Crochemore, Maxime

AU - Landau, Gad M.

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N1 - 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.

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KW - Design and analysis of algorithms

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BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Amir A, Butman A, Crochemore M, Landau GM, Schaps M. Two-dimensional pattern matching with rotations. In Baeza-Yates R, Chavez E, Crochemore M, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2003. p. 17-31. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-44888-8_2

Two-dimensional pattern matching with rotations

Abstract

Publication series

Bibliographical note

Funding

Keywords

Access to Document

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