New Partially Labelled Tree Similarity Measure: A Case Study

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6218)


Trees are a powerful data structure for representing data for which hierarchical relations can be defined. They have been applied in a number of fields like image analysis, natural language processing, protein structure, or music retrieval, to name a few. Procedures for comparing trees are very relevant in many task where tree representations are involved. The computation of these measures is usually a time consuming tasks and different authors have proposed algorithms that are able to compute them in a reasonable time, through approximated versions of the similarity measure. Other methods require that the trees are fully labelled for the distance to be computed. In this paper, a new measure is presented able to deal with trees labelled only at the leaves, that runs in O(|T A |×|T B |) time. Experiments and comparative results are provided.


Tree edit distance multimedia music comparison and retrieval 


  1. 1.
    Bille, P.: A survey on tree edit distance and related problems. Theorical Computer Science 337(1-3), 217–239 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Finkel, R.A., Bentley, J.L.: Quad trees: A data structure for retrieval on composite keys. Acta Inf. 4, 1–9 (1974)zbMATHCrossRefGoogle Scholar
  3. 3.
    Habrard, A., Iñesta, J.M., Rizo, D., Sebban, M.: Melody recognition with learned edit distances. In: da Vitoria Lobo, N., Kasparis, T., Roli, F., Kwok, J.T., Georgiopoulos, M., Anagnostopoulos, G.C., Loog, M. (eds.) S+SSPR 2008. LNCS, vol. 5342, pp. 86–96. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Illescas, P.R., Rizo, D., Iñesta, J.M.: Harmonic, melodic, and functional automatic analysis. In: Proceedings of the 2007 International Computer Music Conferrence, vol. I, pp. 165–168 (2007)Google Scholar
  5. 5.
    Isert, C.: The editing distance between trees. Technical report, Institut für Informatik, Technische Universität München (1999)Google Scholar
  6. 6.
    Jiang, T., Wang, L., Zhang, K.: Alignment of trees – an alternative to tree edit. Theoretical Computer Science 143(1), 137–148 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kuboyama, T., Shin, K., Miyahara, T.: A hierarchy of tree edit distance measures. Theoretical Computer Science and its Applications (2005)Google Scholar
  8. 8.
    Marcus, M., Kim, G., Marcinkiewicz, M.A., Macintyre, R., Bies, A., Ferguson, M., Katz, K., Schasberger, B.: The penn treebank: Annotating predicate argument structure. In: ARPA Human Language Technology Workshop, pp. 114–119 (1994)Google Scholar
  9. 9.
    Rizo, D., Lemström, K., Iñesta, J.M.: Tree representation in combined polyphonic music comparison. In: Ystad, S., Kronland-Martinet, R., Jensen, K. (eds.) CMMR 2008. LNCS, vol. 5493, pp. 177–195. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Rizo, D., Moreno-Seco, F., JIñesta, J.M.: Tree-structured representation of musical information. In: Perales, F.J., Campilho, A.C., Pérez, N., Sanfeliu, A. (eds.) IbPRIA 2003. LNCS (LNAI), vol. 2652, pp. 838–846. Springer, Heidelberg (2003)Google Scholar
  11. 11.
    Russell, R.B., Barton, G.J.: Multiple protein sequence alignment from tertiary structure comparison: Assignment of global and residue confidence levels. Proteins: Structure, Function, and Bioinformatics 14, 309–323 (2004)Google Scholar
  12. 12.
    Selkow, S.M.: The tree-to-tree editing problem. Information Processing Letters 6(6), 184–186 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Tai, K.-C.: The tree-to-tree correction problem. J. ACM 26(3), 422–433 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Valiente, G.: An efficient bottom-up distance between trees. International Symposium on String Processing and Information Retrieval, 0,212 (2001)Google Scholar
  15. 15.
    Zhang, K., Shasha, D.: Simple fast algorithms for the editing distance between trees and related problems. SIAM J. Comput. 18(6), 1245–1262 (1989)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Dept. Lenguajes y Sistemas InformáticosUniversidad de AlicanteAlicanteSpain

Personalised recommendations