Approximate Function Matching under δ- and γ- Distances

  • Juan Mendivelso
  • Inbok Lee
  • Yoan J. Pinzón
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7608)


This paper defines a new string matching problem by combining two paradigms: function matching and δγ-matching. The result is an approximate variant of function matching where two equal-length strings X and Y match if there exists a function that maps X to a string X′ such that X′ and Y are δγ- similar. We propose an O(nm) algorithm for finding all the matches of a pattern P 1 …m in a text T 1 …n .


combinatorial algorithms δ–matching γ–matching δγ–matching function matching 


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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)zbMATHCrossRefGoogle Scholar
  3. 3.
    Amir, A., Nor, I.: Generalized function matching. Journal of Discrete Algorithms 5(3), 514–523 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Apostolico, A., Galil, Z.: Pattern matching algorithms. Oxford University Press, USA (1997)zbMATHCrossRefGoogle Scholar
  5. 5.
    Baker, B.S.: A theory of parameterized pattern matching: algorithms and applications. In: Proc. 25th Annual Symposium on Theory of Computing (1993)Google Scholar
  6. 6.
    Baker, B.S.: Parameterized pattern matching by Boyer-Moore-type algorithms. In: Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, p. 550. Society for Industrial and Applied Mathematics (1995)Google Scholar
  7. 7.
    Cantone, D., Cristofaro, S., Faro, S.: Efficient Algorithms for the δ-Approximate String Matching Problem in Musical Sequences. In: Proc. of the Prague Stringology Conference (2004)Google Scholar
  8. 8.
    Clifford, R., Harrow, A.W., Popa, A., Sach, B.: Generalised Matching. In: Karlgren, J., Tarhio, J., Hyyrö, H. (eds.) SPIRE 2009. LNCS, vol. 5721, pp. 295–301. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Clifford, R., Sach, B.: Permuted function matching. Information Processing Letters 110(22), 1012–1015 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Crochemore, M., Iliopoulos, C.S., Lecroq, T., Pinzon, Y.J., Plandowski, W., Rytter, W.: Occurrence and Substring Heuristics for d-Matching. Fundamenta Informaticae 56(1), 1–21 (2003)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Crochemore, M., Iliopoulos, C.S., Lecroq, T., Plandowski, W., Rytter, W.: Three Heuristics for δ-Matching: δ-BM Algorithms. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 178–189. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Crochemore, M., Iliopoulos, C.S., Navarro, G., Pinzon, Y.J., Salinger, A.: Bit-parallel (δ, γ)-Matching and Suffix Automata. Journal of Discrete Algorithms 3(2-4), 198–214 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Fredriksson, K., Mäkinen, V., Navarro, G.: Flexible music retrieval in sublinear time. In: Proceedings of the 10th Prague Stringology Conference (PSC 2005), pp. 174–188 (2005)Google Scholar
  14. 14.
    Hazay, C., Lewenstein, M., Sokol, D.: Approximate parameterized matching. ACM Transactions on Algorithms (TALG) 3(3), 29 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lee, I., Mendivelso, J., Pinzón, Y.J.: δγ – Parameterized Matching. In: Amir, A., Turpin, A., Moffat, A. (eds.) SPIRE 2008. LNCS, vol. 5280, pp. 236–248. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Reiser, A.: A linear selection algorithm for sets of elements with weights. Inf. Process. Lett. 7(3), 159–162 (1978)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Juan Mendivelso
    • 1
  • Inbok Lee
    • 2
  • Yoan J. Pinzón
    • 1
  1. 1.Department of Computer Science and Industrial Engineering, Research Group on Algorithms and Combinatorics (ALGOS-UN)Universidad Nacional de ColombiaColombia
  2. 2.School of Electronic, Telecommunication, and Computer EngineeringKorea Aerospace UniversityRepublic of Korea

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