Improved MAX SNP-Hard Results for Finding an Edit Distance between Unordered Trees

  • Kouichi Hirata
  • Yoshiyuki Yamamoto
  • Tetsuji Kuboyama
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6661)


Zhang and Jiang (1994) have shown that the problem of finding an edit distance between unordered trees is MAX SNP-hard. In this paper, we show that this problem is MAX SNP-hard, even if (1) the height of trees is 2, (2) the degree of trees is 2, (3) the height of trees is 3 under a unit cost, and (4) the degree of trees is 2 under a unit cost.


Unit Cost Edit Distance Edit Operation Polynomial Time Approximation Scheme Left Child 
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.
    Bille, P.: A survey on tree edit distance and related problems. Theoret. Comput. Sci. 337, 217–239 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Demaine, E.D., Mozes, S., Rossman, B., Weimann, O.: An optimal decomposition algorithm for tree edit distance. ACM Trans. Algorithms 6 (2009)Google Scholar
  3. 3.
    Jiang, T., Wang, L., Zhang, K.: Alignment of trees – an alternative to tree edit. Theoret. Comput. Sci. 143, 137–148 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Kann, V.: Maximum bounded 3-demensional matching is MAX SNP-complete. Inform. Process. Let. 37, 27–35 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation and complexity. J. Comput. System Sci. 43, 425–440 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Shasha, D., Wang, J.T.-L., Zhang, K., Shih, F.Y.: Exact and approximate algorithms for unordered tree matching. IEEE Trans. Sys. Man. and Cybernet. 24, 668–678 (1994)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Tai, K.-C.: The tree-to-tree correction problem. J. ACM 26, 422–433 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Zhang, K., Jiang, T.: Some MAX SNP-hard results concerning unordered labeled trees. Inform. Process. Let. 49, 249–254 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Zhang, K., Shasha, D.: Simple fast algorithms for the editing distance between trees and related problems. SIAM J. Comput. 18, 1245–1262 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Zhang, K., Statman, R., Shasha, D.: On the editing distance between unordered labeled trees. Inform. Process. Let. 42, 133–139 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Zhang, K., Wang, J., Shasha, D.: On the editing distance between undirected acyclic graphs. Int. J. Found. Comput. Sci. 7, 43–58 (1995)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kouichi Hirata
    • 1
  • Yoshiyuki Yamamoto
    • 2
  • Tetsuji Kuboyama
    • 3
  1. 1.Department of Artificial IntelligenceKyushu Institute of TechnologyIizukaJapan
  2. 2.Graduate School of Computer Science and Systems EngineeringKyushu Institute of TechnologyIizukaJapan
  3. 3.Computer CenterGakushuin UniversityToshimaJapan

Personalised recommendations