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An Efficient Algorithm for δ-Approximate Matching with α-Bounded Gaps in Musical Sequences

  • Domenico Cantone
  • Salvatore Cristofaro
  • Simone Faro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)

Abstract

We present a new efficient algorithm for the δ-approximate matching problem with α-bounded gaps. The δ-approximate matching problem, recently introduced in connection with applications in music retrieval, generalizes the exact string matching problem by relaxing the notion of matching. Here we consider the case in which matchings may contain bounded gaps.

An extensive comparison with the only (to our knowledge) other solution existing in the literature for the same problem, due to Crochemore et al., indicates that our algorithm is more efficient, especially in the cases of large alphabets and long patterns. In addition, our algorithm computes the total number of approximate matchings for each position of the text, requiring only \({\mathcal O}(m\alpha)\)-space, where m is the length of the pattern.

Keywords

approximate string matching experimental algorithms musical information retrieval 

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References

  1. 1.
    Cambouropoulos, E., Crochemore, M., Iliopoulos, C.S., Mouchard, L., Pinzon, Y.J.: Algorithms for computing approximate repetitions in musical sequences. In: Raman, R., Simpson, J. (eds.) Proceedings of the 10th Australasian Workshop On Combinatorial Algorithms, Perth, WA, Australia, pp. 129–144 (1999)Google Scholar
  2. 2.
    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, Czech Technical University, Prague, Czech Republic, pp. 69–82 (2004)Google Scholar
  3. 3.
    Crawford, T., Iliopoulos, C., Raman, R.: String matching techniques for musical similarity and melodic recognition. Computing in Musicology 11, 71–100 (1998)Google Scholar
  4. 4.
    Crochemore, M., Iliopoulos, C., Makris, C., Rytter, W., Tsakalidis, A., Tsichlas, K.: Approximate string matching with gaps (2002)Google Scholar
  5. 5.
    Crochemore, M., Iliopoulos, C.S., Lecroq, T., Pinzon, Y.J.: Approximate string matching in musical sequences. In: Balík, M., Šimánek, M. (eds.) Proceedings of the Prague Stringology Conference 2001, Prague, Czech Republic, pp. 26–36 (2001), Annual Report DC–2001–06Google Scholar
  6. 6.
    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
  7. 7.
    Crochemore, M., Iliopoulos, C.S., Pinzon, Y.J., Reid, J.F.: A fast and practical bit-vector algorithm for the longest common subsequence problem. In: Brankovic, L., Ryan, J. (eds.) Proceedings of the 11th Australasian Workshop On Combinatorial Algorithms, Hunter Valley, Australia, pp. 75–86 (2000)Google Scholar
  8. 8.
    Karhumäki, J., Plandowski, W., Rytter, W.: Pattern-matching problems for two-dimensional images described by finite automata. Nordic J. Comput. 7(1), 1–13 (2000)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Karlin, S., Morris, M., Ghandour, G., Leung, M.Y.: Efficient algorithms for molecular sequence analysis. Proceedings of the National Academy of Science 85, 841–845 (1988)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Domenico Cantone
    • 1
  • Salvatore Cristofaro
    • 1
  • Simone Faro
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità di CataniaCataniaItaly

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