Two Dimensional Parameterized Matching

  • Carmit Hazay
  • Moshe Lewenstein
  • Dekel Tsur
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3537)


Two equal length strings, or two equal sized two dimensional texts, parameterize match (p-match) if there is a one-one mapping (relative to the alphabet) of their characters. Two dimensional parameterized matching is the task of finding all m × m substrings of an n× n text that p-match to an m× m pattern. This models, for example, searching for color images with changing of color maps. We present an algorithm that solves the two dimensional parameterized matching problem in O(n 2+m 2.5·polylog(m)) time.


Match Problem Distinct Character Function Match Parameterized Match Sweep Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alon, N., Naor, M.: Derandomization, witnesses for boolean matrix multiplication and construction of perfect hash functions. Algorithmica 16, 434–449 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Amir, A., Aumann, Y., Cole, R., Lewenstein, M., Porat, E.: Function matching: Algorithms, applications and a lower bound. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 929–942. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Amir, A., Benson, G., Farach, M.: An alphabet independent approach to two dimensional pattern matching. SIAM J. on Computing 23(2), 313–323 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Amir, A., Church, K.W., Dar, E.: Separable attributes: a technique for solving the submatrices character count problem. In: Proc. 13th Symposium on Discrete Algorithms (SODA), pp. 400–401 (2002)Google Scholar
  5. 5.
    Amir, A., Cole, R.: Personal communications (2004)Google Scholar
  6. 6.
    Amir, A., Farach, M., Muthukrishnan, S.: Alphabet dependence in parameterized matching. Information Processing Letters 49, 111–115 (1994)zbMATHCrossRefGoogle Scholar
  7. 7.
    Apostolico, A., Erdös, P., Lewenstein, M.: Parameterized matching with mismatches (manuscript)Google Scholar
  8. 8.
    Babu, G.P., Mehtre, B.M., Kankanhalli, M.S.: Color indexing for efficient image retrieval. Multimedia Tools and Applications 1(4), 327–348 (1995)CrossRefGoogle Scholar
  9. 9.
    Baker, B.S.: A theory of parameterized pattern matching: algorithms and applications. In: Proc. 25th ACM Symposium on the Theory of Computation (STOC), pp. 71–80 (1993)Google Scholar
  10. 10.
    Baker, B.S.: Parameterized string pattern matching. J. Comput. Systems Sci. 52(1), 28–42 (1996)zbMATHCrossRefGoogle Scholar
  11. 11.
    Baker, B.S.: Parameterized duplication in strings: Algorithms and an application to software maintenance. SIAM J. on Computing 26(5), 1343–1362 (1997)zbMATHCrossRefGoogle Scholar
  12. 12.
    Cole, R., Hariharan, R.: Faster suffix tree construction with missing suffix links. In: Proc. 32nd ACM Symposium on the Theory of Computation (STOC), pp. 407–415 (2000)Google Scholar
  13. 13.
    Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proc. 16th ACM Symposium on Theory of Computing (STOC), vol. 67, pp. 135–143 (1984)Google Scholar
  14. 14.
    Gupta, P., Janardan, R., Smid, M.: Further results on generalized intersection searching problems: Counting, reporting, and dynamization. J. of Algorithms 19(2), 282–317 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Hazay, C., Lewenstein, M., Sokol, D.: Approximate parameterized matching. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 414–425. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Kosaraju, S.R.: Faster algorithms for the construction of parameterized suffix trees. In: Proc. 36th Symposium on Foundation of Computer Science (FOCS), pp. 631–637 (1995)Google Scholar
  17. 17.
    Swain, M., Ballard, D.: Color indexing. International Journal of Computer Vision 7(1), 11–32 (1991)CrossRefGoogle Scholar
  18. 18.
    Vishkin, U.: Optimal parallel pattern matching in strings. In: Brauer, W. (ed.) ICALP 1985. LNCS, vol. 194, pp. 91–113. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  19. 19.
    Vishkin, U.: Deterministic sampling — a new technique for fast pattern matching. SIAM J. on Computing 20, 303–314 (1991)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Carmit Hazay
    • 1
  • Moshe Lewenstein
    • 1
  • Dekel Tsur
    • 2
  1. 1.Bar-Ilan University 
  2. 2.University of CaliforniaSan Diego

Personalised recommendations