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Optimal Exact and Fast Approximate Two Dimensional Pattern Matching Allowing Rotations

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Combinatorial Pattern Matching (CPM 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2373))

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Abstract

We give fast filtering algorithms to search for a 2-dimensional pattern in a 2-dimensional text allowing any rotation of the pattern. We consider the cases of exact and approximate matching under several matching models, improving the previous results. For a text of size n × n characters and a pattern of size m × m characters, the exact matching takes average time O(n 2 log m/m 2), which is optimal. If we allow k mismatches of characters, then our best algorithm achieves O(n 2 k log m/m 2) average time, for reasonable k values. For large k, we obtain an O(n 2 k 3/2 √log m/m) average time algorithm. We generalize the algorithms for the matching model where the sum of absolute differences between characters is at most k. Finally, we show how to make the algorithms optimal in the worst case, achieving the lower bound Ω(n 2 m 3).

Work supported by ComBi and the Academy of Finland.

Partially supported by the Millenium Center for Web Research.

Work supported by the Academy of Finland.

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Author information

Authors and Affiliations

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

    Kimmo Fredriksson & Esko Ukkonen

  2. Department of Computer Science, University of Chile, Chile

    Gonzalo Navarro

Authors
  1. Kimmo Fredriksson
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  2. Gonzalo Navarro
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  3. Esko Ukkonen
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Editor information

Editors and Affiliations

  1. Department of Electrial Engineering and Computer Science, University of Padova, Via Gradenigo 6/A, 35131, Padova, Italy

    Alberto Apostolico

  2. Department of Informatics, Kyushu University, Fukuoka 812-8581, Japan

    Masayuki Takeda

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© 2002 Springer-Verlag Berlin Heidelberg

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Fredriksson, K., Navarro, G., Ukkonen, E. (2002). Optimal Exact and Fast Approximate Two Dimensional Pattern Matching Allowing Rotations. In: Apostolico, A., Takeda, M. (eds) Combinatorial Pattern Matching. CPM 2002. Lecture Notes in Computer Science, vol 2373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45452-7_20

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  • DOI: https://doi.org/10.1007/3-540-45452-7_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43862-5

  • Online ISBN: 978-3-540-45452-6

  • eBook Packages: Springer Book Archive

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