Sweepline the Music

  • Esko Ukkonen
  • Kjell Lemström
  • Veli Mäkinen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2598)


The problem of matching sets of points or sets of horizontal line segments in plane under translations is considered. For finding the exact occurrences of a point set of size m within another point set of size n we give an algorithm with running time O(mn), and for finding partial occurrences an algorithm with running time O(mnlogm). To find the largest overlap between two line segment patterns we develop an algorithm with running time O(mnlog(mn)). All algorithms are based on a simple sweepline traversal of one of the patterns in the lexicographic order. The motivation for the problems studied comes from music retrieval and analysis.


Line Segment Turning Point Pattern Match Edit Distance Priority Queue 
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.
    H. Alt and L. Guibas. Discrete geometric shapes: Matching, interpolation, and approximation. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 121–153. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 1999.Google Scholar
  2. 2.
    H. Alt, K. Mehlhorn, H. Wagener, and E. Welzl. Congruence, similarity and symmetries of geometric objects. Discrete Comput. Geom., 3:237–256, 1988.zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    M. D. Atkinson. An optimal algorithm for geometric congruence. J. Algorithms, 8:159–172, 1997.CrossRefGoogle Scholar
  4. 4.
    J. L. Bentley and T. A. Ottmann. Algorithms for reporting and counting geometric intersections. IEEE Transactions on Computers, C-28:643–647, September 1979.Google Scholar
  5. 5.
    L. P. Chew and K. Kedem. Improvements on geometric pattern matching problems. In Proceedings of the Scandinavian Workshop Algomthm Theory (SWAT), pages 318–325, 1992.Google Scholar
  6. 6.
    M. Clausen, R. Engelbrecht, D. Meyer, and J. Schmitz. Proms: A web-based tool for searching in polyphonic music. In Proceedings of the International Symposium on Music Information Retrieval (ISMIR’2000), 2000.Google Scholar
  7. 7.
    R. Cole and R. Hariharan. Verifying candidate matches in sparse and wildcard matching. In Proceedings of the 34th ACM Symposium on Theory of Computing, pages 592–601. ACM Press, 2002.Google Scholar
  8. 8.
    M. J. Dovey. A technique for “regular expression” style searching in polyphonic music. In the 2nd Annual International Symposium on Music Information Retrieval (ISMIR’2001), pages 179–185, 2001.Google Scholar
  9. 9.
    A. Efrat and A. Itai. Improvements on bottleneck matching and related problems using geometry. In Proceedings of the twelfth annual symposium on Computational geometry, pages 301–310. ACM Press, 1996.Google Scholar
  10. 10.
    A. Ghias, J. Logan, D. Chamberlin, and B. C. Smith. Query by humming-musical information retrieval in an audio database. In ACM Multimedia 95 Proceedings, pages 231–236, 1995. Electronic Proceedings:
  11. 11.
    J. Holub, C. S. Iliopoulos, and L. Mouchard. Distributed string matching using finite automata. Journal of Automata, Languages and Combinatorics, 6(2):191–204, 2001.zbMATHMathSciNetGoogle Scholar
  12. 12.
    D. Huttenlocher and S. Ullman. Recognizing solid objects by alignment with an image. Intern. J. Computer Vision, 5:195–212, 1990.CrossRefGoogle Scholar
  13. 13.
    K. Lemström. String Matching Techniques for Music Retrieval. PhD thesis, University of Helsinki, Department of Computer Science, 2000. Report A-2000-4.Google Scholar
  14. 14.
    K. Lemström and S. Perttu. SEMEX-an efficient music retrieval prototype. In Proceedings of the International Symposium on Music Information Retrieval (ISMIR’2000), 2000.Google Scholar
  15. 15.
    K. Lemström and J. Tarhio. Detecting monophonic patterns within polyphonic sources. In ontent-Based Multimedia Information Access Conference Proceedings (RIAO’2000), pages 1261–1279, 2000.Google Scholar
  16. 16.
    K. Lemström and E. Ukkonen. Including interval encoding into edit distance based music comparison and retrieval. In Proceedings of the AISB’2000 Symposium on Creative & Cultural Aspects and Applications of AI & Cognitive Science, pages 53–60, 2000.Google Scholar
  17. 17.
    V. Mäkinen, G. Navarro, and E. Ukkonen. Algorithms for transposition invariant string matching. Technical Report TR/DCC-2002-5, Department of Computer Science, University of Chile, 2002.Google Scholar
  18. 18.
    R. J. McNab, L. A. Smith, D. Bainbridge, and I. H. Witten. The New Zealand digital library MELody in DEX. D-Lib Magazine, 1997.
  19. 19.
    D. Meredith, G. A. Wiggins, and K. Lemström. Pattern induction and matching in polyphonic music and other multi-dimensional data. In the 5th World Multi-Conference on Systemics, Cybernetics and Informatics (SCI’2001), volume X, pages 61–66, 2001.Google Scholar
  20. 20.
    M. Mongeau and D. Sankoff. Comparison of musical sequences. Computers and the Humanities, 24:161–175, 1990.CrossRefGoogle Scholar
  21. 21.
    G. A. Wiggins, K. Lemström, and D. Meredith. SIA(M)-a family of efficient algorithms for translation invariant pattern matching in multidimensional datasets. Manuscript (submitted), September 2002.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Esko Ukkonen
    • 1
  • Kjell Lemström
    • 1
  • Veli Mäkinen
    • 1
  1. 1.Department of Computer ScienceUniversity of HelsinkiHelsinkiFinland

Personalised recommendations