, Volume 15, Issue 3, pp 205–222

A constrained edit distance between unordered labeled trees

  • Kaizhong Zhang


This paper considers the problem of computing a constrained edit distance between unordered labeled trees. The problem of approximate unordered tree matching is also considered. We present dynamic programming algorithms solving these problems in sequential timeO(|T1|×|T2|×(deg(T1)+deg(T2))× log2(deg(T1)+deg(T2))). Our previous result shows that computing the edit distance between unordered labeled trees is NP-complete.

Key words

Unordered trees Constrained edit distance Approximate tree matching 


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  1. [1]
    A. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy, Proof verification and hardness of approximation problems,Proc. 33rd IEEE Symp. on the Foundation of Computer Science, 1992, pp. 14–23.Google Scholar
  2. [2]
    G. M. Landau and U. Vishkin, Fast parallel and serial approximate string matching,J. Algorithms,10 (1989), 157–169.Google Scholar
  3. [3]
    P. Kilpelainen and H. Mannila, The tree inclusion problem,Proc. Internat. Joint Conf. on the Theory and Practice of Software Development (CAAP '91), 1991, Vol. 1, pp. 202–214.Google Scholar
  4. [4]
    S. Masuyama, Y. Takahashi, T. Okuyama, and S. Sasaki, On the largest common subgraph problem,Algorithms and Computing Theory, RIMS, Kokyuroku (Kyoto University), 1990, pp. 195–201.Google Scholar
  5. [5]
    P. H. Sellers, The theory and computation of evolutionary distances,J. Algorithms,1 (1980), 359–373.Google Scholar
  6. [6]
    B. Shapiro and K. Zhang, Comparing multiple RNA secondary structures using tree comparisons,Comput. Appl. Biosci.,6(4) (1990), 309–318.Google Scholar
  7. [7]
    F. Y. Shih, Object representation and recognition using mathematical morphology model,J. System Integration,1 (1991), 235–256.Google Scholar
  8. [8]
    F. Y. Shih and O. R. Mitchell, Threshold decomposition of grayscale morphology into binary morphology,IEEE Trans. Pattern Anal. Mach. Intell.,11 (1989), 31–42.Google Scholar
  9. [9]
    K. C. Tai, The tree-to-tree correction problem,J. Assoc. Comput. Mach.,26 (1979), 422–433.Google Scholar
  10. [10]
    Y. Takahashi, Y. Satoh, H. Suzuki, and S. Sasaki, Recognition of largest common structural fragment among a variety of chemical structures,Anal. Sci.,3 (1987), 23–28.Google Scholar
  11. [11]
    E. Tanaka and K. Tanaka, The tree-to-tree editing problem,Internat. J. Pattern Recog. Artificial Intell.,2(2) (1988), 221–240.Google Scholar
  12. [12]
    R. E. Tarjan,Data Structures and Network Algorithms, CBMS-NSF Regional Conference Series in Applied Mathematics, CBMS, Washington, DC, 1983.Google Scholar
  13. [13]
    E. Ukkonen, Finding approximate patterns in strings,J. Algorithms,6 (1985), 132–137.Google Scholar
  14. [14]
    J. T. L. Wang, Kaizhong Zhang, Karpjoo Jeong, and D. Shasha, ATBE: a system for approximate tree matching,IEEE Trans. Knowledge Data Engrg,6(4) (1994), 559–571.Google Scholar
  15. [15]
    Kaizhong Zhang, Algorithms for the Constrained Editing Distance Between Ordered Labeled Trees and Related Problems, Technical Report No. 361, Department of Computer Science, University of Western Ontario, 1993.Google Scholar
  16. [16]
    Kaizhong Zhang and Tao Jiang, Some MAX SNP-hard results concerning unordered labeled trees,Inform. Process. Lett.,49 (1994), 249–254.Google Scholar
  17. [17]
    Kaizhong Zhang and D. Shasha, Simple fast algorithms for the editing distance between trees and related problems,SIAM J. Comput.,18(6) (1989), 1245–1262.Google Scholar
  18. [18]
    Kaizhong Zhang, D. Shasha, and J. Wang, Approximate tree matching in the presence of variable length don't cares,J. Algorithms,16 (1994), 33–66.Google Scholar
  19. [19]
    Kaizhong Zhang, R. Statman and D. Shasha, On the editing distance between unordered labeled trees,Inform. Process. Lett.,42 (1992), 133–139.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1996

Authors and Affiliations

  • Kaizhong Zhang
    • 1
  1. 1.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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