Abstract
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(|T 1|×|T 2|×(deg(T 1)+deg(T 2))× log2(deg(T 1)+deg(T 2))). Our previous result shows that computing the edit distance between unordered labeled trees is NP-complete.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
G. M. Landau and U. Vishkin, Fast parallel and serial approximate string matching,J. Algorithms,10 (1989), 157–169.
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.
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.
P. H. Sellers, The theory and computation of evolutionary distances,J. Algorithms,1 (1980), 359–373.
B. Shapiro and K. Zhang, Comparing multiple RNA secondary structures using tree comparisons,Comput. Appl. Biosci.,6(4) (1990), 309–318.
F. Y. Shih, Object representation and recognition using mathematical morphology model,J. System Integration,1 (1991), 235–256.
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.
K. C. Tai, The tree-to-tree correction problem,J. Assoc. Comput. Mach.,26 (1979), 422–433.
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.
E. Tanaka and K. Tanaka, The tree-to-tree editing problem,Internat. J. Pattern Recog. Artificial Intell.,2(2) (1988), 221–240.
R. E. Tarjan,Data Structures and Network Algorithms, CBMS-NSF Regional Conference Series in Applied Mathematics, CBMS, Washington, DC, 1983.
E. Ukkonen, Finding approximate patterns in strings,J. Algorithms,6 (1985), 132–137.
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.
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.
Kaizhong Zhang and Tao Jiang, Some MAX SNP-hard results concerning unordered labeled trees,Inform. Process. Lett.,49 (1994), 249–254.
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.
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.
Kaizhong Zhang, R. Statman and D. Shasha, On the editing distance between unordered labeled trees,Inform. Process. Lett.,42 (1992), 133–139.
Author information
Authors and Affiliations
Additional information
Communicated by H. N. Gabow.
This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. OGP0046373.
Rights and permissions
About this article
Cite this article
Zhang, K. A constrained edit distance between unordered labeled trees. Algorithmica 15, 205–222 (1996). https://doi.org/10.1007/BF01975866
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01975866