Sublinear Algorithms for Parameterized Matching

  • Leena Salmela
  • Jorma Tarhio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4009)


Two strings parameterize match if there is a bijection that transforms the first string character by character into the second string. This problem has been studied in both one and two dimensions but the research has been centered on developing algorithms with good worst-case performance. We present algorithms that solve this problem in sublinear time on average for moderately repetitive patterns.


String Match Repetitive Pattern Random Text Read Character Parameterized Match 


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  1. 1.
    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
  2. 2.
    Amir, A., Farach, M., Muthukrishnan, S.: Alphabet dependence in parameterized matching. Information Processing Letters 49(3), 111–115 (1994)CrossRefMATHGoogle Scholar
  3. 3.
    Baeza-Yates, R.: Improved string searching. Software – Practice and Experience 19(3), 257–271 (1989)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Baeza-Yates, R., Gonnet, G.: A new approach to text searching. Communications of ACM 35(10), 74–82 (1992)CrossRefGoogle Scholar
  5. 5.
    Baker, B.S.: A theory of parameterized pattern matching: algorithms and applications. In: Proceedings of the 25th ACM Symposium on the Theory of Computation, pp. 71–80 (1993)Google Scholar
  6. 6.
    Baker, B.S.: Parameterized pattern matching by Boyer-Moore-type algorithms. In: Proceedings of the 6th Annual ACM Symposium on Theory of Computing, pp. 541–550 (1995)Google Scholar
  7. 7.
    Baker, B.S.: Parameterized diff. In: Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 854–855 (1999)Google Scholar
  8. 8.
    Boyer, R., Moore, J.: A fast string searching algorithm. Communications of the ACM 20(10), 762–772 (1977)CrossRefGoogle Scholar
  9. 9.
    Cole, R., Hariharan, R.: Faster suffix tree construction with missing suffix links. In: Proceedings of the 32nd ACM Symposium on the Theory of Computation (STOC), pp. 407–415 (2000)Google Scholar
  10. 10.
    Crochemore, M., Lecroq, T., Czumaj, A., Gąsieniec, L., Jarominek, S., Plandowski, W.: Speeding up two string-matching algorithms. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 589–600. Springer, Heidelberg (1992)Google Scholar
  11. 11.
    Fredriksson, K., Mozgovoy, M.: Sublinear parameterized single and multiple string matching. Technical Report A-2006-2, Department of Computer Science, University of Joensuu (2006)Google Scholar
  12. 12. Copyright-free photo archive: Public domain photos and images (2000),
  13. 13.
    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
  14. 14.
    Hazay, C., Lewenstein, M., Tsur, D.: Two dimensional parameterized matching. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 266–279. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Horspool, N.: Practical fast searching in strings. Software – Practise and Experience 10, 501–506 (1980)CrossRefGoogle Scholar
  16. 16.
    Idury, R.M., Schäffer, A.A.: Multiple matching of parameterized patterns. Theorethical Computer Science 154(2), 203–224 (1996)CrossRefMATHGoogle Scholar
  17. 17.
    Knuth, D.E., Morris, J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM Journal of Computing 6, 323–350 (1977)CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    Kosaraju, S.R.: Faster algorithms for the construction of parameterized suffix trees. In: Proceedings of the 36th Symposium on Foundation of Computer Science (FOCS), pp. 631–637 (1995)Google Scholar
  19. 19.
    Kreher, D.L., Stinson, D.R.: Combinatorial Algorithms: Generation, Enumeration and Search. CRC Press, Boca Raton (1999)MATHGoogle Scholar
  20. 20.
    Tarhio, J.: A sublinear algorithm for two dimensional string matching. Pattern Recognition Letters 17, 833–838 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Leena Salmela
    • 1
  • Jorma Tarhio
    • 1
  1. 1.Helsinki University of Technology 

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