Skip to main content

Faster Two Dimensional Pattern Matching with Rotations

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3109))

Abstract

The most efficient currently known algorithms for two dimensional matching with rotation have a worst case time complexity of O(n 2 m 3), where the size of the text is n 2 and the size of the pattern is m 2. In this paper we present two algorithms for the two dimensional rotated matching problem whose running time is O(n 2 m 2). The preprocessing time of the first algorithms is O(m 5) and the preprocessing time of the second algorithm is O(m 4).

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aho, A.V., Corasick, M.J.: Efficient string matching. Comm. ACM 18(6), 333–340 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. Amir, A., Butman, A., Crochemore, M., Landau, G.M., Schaps, M.: Two-dimensional pattern matching with rotations. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 17–31. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Amir, A., Butman, A., Lewenstein, M.: Real scaled matching. Information Processing Letters 70(4), 185–190 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  4. Amir, A., Butman, A., Lewenstein, M., Porat, E.: Real two dimensional scaled matching. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 353–364. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Amir, A., Farach, M.: Two dimensional dictionary matching. Information Processing Letters 44, 233–239 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Amir, A., Landau, G.: Fast parallel and serial multidimensional approximate array matching. Theoretical Computer Science 81, 97–115 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  7. Apostolico, A., Galil, Z. (eds.): Pattern Matching Algorithms. Oxford University Press, Oxford (1997)

    MATH  Google Scholar 

  8. Crochemore, M., Rytter, W.: Text Algorithms. Oxford University Press, Oxford (1994)

    MATH  Google Scholar 

  9. Fischer, M.J., Paterson, M.S.: String matching and other products. Complexity of Computation. In: Karp, R.M. (ed.) SIAM-AMS Proceedings, 7th edn., pp. 113–125 (1974)

    Google Scholar 

  10. Fredriksson, K., Mäkinen, V., Navarro, G.: Rotation and lighting invariant template matching. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 39–48. Springer, Heidelberg (2004), http://www.dcc.uchile.cl/~gnavarro/ps/latin04.ps.gzx

    Chapter  Google Scholar 

  11. Fredriksson, K., Navarro, G., Ukkonen, E.: An index for two dimensional string matching allowing rotations. In: Watanabe, O., Hagiya, M., Ito, T., van Leeuwen, J., Mosses, P.D. (eds.) TCS 2000. LNCS, vol. 1872, pp. 59–75. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Fredriksson, K., Navarro, G., Ukkonen, E.: Optimal exact and fast approximate two dimensional pattern matching allowing rotations. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 235–248. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Fredriksson, K., Ukkonen, E.: A rotation invariant filter for two-dimensional string matching. In: Farach-Colton, M. (ed.) CPM 1998. LNCS, vol. 1448, pp. 118–125. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Fredriksson, K., Ukkonen, E.: A rotation invariant filter for two-dimensional string matching. In: Farach-Colton, M. (ed.) CPM 1998. LNCS, vol. 1448, pp. 118–125. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  15. Fredriksson, K., Ukkonen, E.: Combinatorial methods for approximate pattern matching under rotations and translations in 3d arrays. In: Proc. 7th Symposium on String Processing and Information Retrieval (SPIRE 2000), pp. 96–104. IEEE CS Press, Los Alamitos (2000)

    Chapter  Google Scholar 

  16. Giancarlo, R., Grossi, R.: On the construction of classes of suffix trees for square matrices: Algorithms and applications. Information and Computation 130(2), 151–182 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  17. Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  18. Landau, G.M., Vishkin, U.: Pattern matching in a digitized image. Algorithmica 12(3/4), 375–408 (1994)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Amir, A., Kapah, O., Tsur, D. (2004). Faster Two Dimensional Pattern Matching with Rotations. In: Sahinalp, S.C., Muthukrishnan, S., Dogrusoz, U. (eds) Combinatorial Pattern Matching. CPM 2004. Lecture Notes in Computer Science, vol 3109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27801-6_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-27801-6_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22341-2

  • Online ISBN: 978-3-540-27801-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics