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Multidimensional String Matching

1999; Kärkkäinen, Ukkonen

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Encyclopedia of Algorithms

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Keywords and Synonyms

Multidimensional array matching; Image matching ; Template registration      

Problem Definition

Given two two-dimensional arrays, the text \( T[1\,\ldots\, n,\,1\,\ldots\, n] \) and the pattern \( P[1\,\ldots\, m,\,1\,\ldots\, m] \), \( m\leq n \), both with element values from alphabet Σ of size σ, the basic two-dimensional string matching (2DSM) problem is to find all occurrences of P in T, i. e., all \( m\times m \) 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), indexed matching (preprocess the text), 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 lead to different variants of the problem. When no distance is explicitly mentioned, the Hamming distance...

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Authors and Affiliations

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

    Juha Kärkkäinen & Esko Ukkonen

Authors
  1. Juha Kärkkäinen
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  2. Esko Ukkonen
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Kärkkäinen, J., Ukkonen, E. (2008). Multidimensional String Matching. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_247

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