Fast Evolutionary Chains

  • Maxime Crochemore
  • Costas S. Iliopoulos
  • Yoan J. Pinzon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1963)


Musical patterns that recur in approximate, rather than identical, form within the body of a musical work are considered to be of considerable importance in music analysis. Here we consider the “evolutionary chain problem”: this is the problem of computing a chain of all “motif” recurrences, each of which is a transformation of (“similar” to) the original motif, but each of which may be progressively further from the original. Here we consider several variants of the evolutionary chain problem and we present efficient algorithms and implementations for solving them.


String algorithms approximate string matching,kw] dynamic programming computer-assisted music analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Apostolico and F. P. Preparata, Optimal Off-line Detection of Repetitions in a String, Theoretical Computer Science, 22 3, pp. 297–315 (1983). 309zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    E. Cambouropoulos, A General Pitch Interval Representation: Theory and Applications, Journal of New Music Research 25, pp. 231–251 (1996). 307CrossRefGoogle Scholar
  3. 3.
    E. Cambouropoulos, T. Crawford and C. S. Iliopoulos, (1999) Pattern Processing in Melodic Sequences: Challenges, Caveats and Prospects. In Proceedings of the AISB’99 Convention (Artificial Intelligence and Simulation of Behaviour), Edinburgh, U.K., pp. 42–47 (1999). 307Google Scholar
  4. 4.
    T. Crawford, C. S. Iliopoulos and R. Raman, String Matching Techniques for Musical Similarity and Melodic Recognition, Computing in Musicology, Vol 11, pp. 73–100 (1998). 307Google Scholar
  5. 5.
    T. Crawford, C. S. Iliopoulos, R. Winder and H. Yu, Approximate musical evolution, in the Proceedings of the 1999 Artificial Intelligence and Simulation of Behaviour Symposium (AISB’99), G. Wiggins (ed), The Society for the Study of Artificial Intelligence and Simulation of Behaviour, Edinburgh, pp. 76–81 (1999). 317Google Scholar
  6. 6.
    M. Crochemore, An optimal algorithm for computing the repetitions in a word, Information Processing Letters 12, pp. 244–250 (1981). 309zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    M. Crochemore, C. S. Iliopoulos and H. Yu, Algorithms for computing evolutionary chains in molecular and musical sequences, Proceedings of the 9-th Australasian Workshop on Combinatorial Algorithms Vol 6, pp. 172–185 (1998). 317Google Scholar
  8. 8.
    C. S. Iliopoulos and L. Mouchard, An O(n log n) algorithm for computing all maximal quasiperiodicities in strings, Proceedings of CATS’99: ”Computing: Australasian Theory Symposium“, Auckland, New Zealand, Lecture Notes in Computer Science, Springer Verlag, Vol 21 3, pp. 262–272 (1999). 309Google Scholar
  9. 9.
    C. S. Iliopoulos, D. W. G. Moore and K. Park, Covering a string, Algorithmica 16, pp. 288–297 (1996). 309zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    C. S. Iliopoulos and Y. J. Pinzon, The Max-Shift Algorithm, submitted. 312Google Scholar
  11. 11.
    G.M. Landau and U. Vishkin, Fast parallel and serial approximate string matching, in Journal of Algorithms 10, pp. 157–169 (1989). 309zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    G. M. Landau and J. P. Schmidt, An algorithm for approximate tandem repeats, in Proc. Fourth Symposium on Combinatorial Pattern Matching, Springer-Verlag Lecture Notes in Computer Science 648, pp. 120–133 (1993). 309Google Scholar
  13. 13.
    G. M. Landau and U. Vishkin, Introducing efficient parallelism into approximate string matching and a new serial algorithm, in Proc. Annual ACM Symposium on Theory of Computing, ACM Press, pp. 220–230 (1986). 311, 312Google Scholar
  14. 14.
    G. Main and R. Lorentz, An O(n log n) algorithm for finding all repetitions in a string, Journal of Algorithms 5, pp. 422–432 (1984). 309zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    E. W. Myers, A Fast Bit-Vector Algorithm for Approximate String Matching Based on Dynamic Progamming, in Journal of the ACM 46 3, pp. 395–415 (1999). 311zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Maxime Crochemore
    • 1
  • Costas S. Iliopoulos
    • 2
  • Yoan J. Pinzon
    • 2
  1. 1.Institut Gaspard-MongeUniversité de Marne-la-ValléeMarne-la-Vallée
  2. 2.Dept. Computer ScienceKing’s College LondonLondonEngland

Personalised recommendations