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Multidimensional String Matching

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 90 Accesses

Years and Authors of Summarized Original Work

  • 1977; Bird

  • 1978; Baker

  • 1991; Amir, Landau

  • 1994; Amir, Benson, Farach

  • 1999; Kärkkäinen, Ukkonen

  • 2000; Baeza-Yates, Navarro

  • 2002; Fredriksson, Navarro, Ukkonen

  • 2006; Amir, Kapah, Tsur

  • 2009; Hundt, Liśkiewicz, Nevries

  • 2010; Amir, Chencinski

Problem Definition

Given two two-dimensional arrays, the text T[1… n, 1… n] and the pattern P[1… m, 1… m], m ≤ n, both with element values from alphabet\(\varSigma\) of size \(\sigma\), the basic two-dimensional string matching (2DSM) problem is to find all occurrences of P in T, i.e., all m × m subarrays of T that are identical to P. In addition to the basic problem, several types of generalizations are considered: approximate matching (allow local errors), invariant matching (allow global transformations), and multidimensional matching.

In approximate matching, an occurrence is a subarray S of the text, whose distance d(S, P) from the pattern does not exceed a threshold k. Different distance measures...

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Recommended Reading

  1. Amir A (2005) Theoretical issues of searching aerial photographs: a bird’s eye view. Int J Found Comput Sci 16(6):1075–1097

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  2. Amir A, Chencinski E (2010) Faster two dimensional scaled matching. Algorithmica 56(2): 214–234

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  3. Amir A, Landau GM (1991) Fast parallel and serial multidimensional approximate array matching. Theor Comput Sci 81(1):97–115

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  5. Amir A, Kapah O, Tsur D (2006) Faster two-dimensional pattern matching with rotations. Theor Comput Sci 368(3):196–204

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Helsinki, Helsinki, Finland

    Juha Kärkkäinen

Authors
  1. Juha Kärkkäinen
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Corresponding author

Correspondence to Juha Kärkkäinen .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Kärkkäinen, J. (2016). Multidimensional String Matching. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_247

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