Abstract
Ordered labeled trees are trees whose nodes are labeled and in which the left-to-right order among siblings is significant. The tree editing problem for input ordered labeled trees T 1 and T 2 is defined as transforming T 1 into T 2 by performing a series of weighted edit operations on T 1 with overall minimum cost. An edit operation can be the deletion, the insertion, and the substitution. Previous results on this problem are only for some special cases and the time complexity depends on the actual distance, though for the more restricted version of degree-2 edit distance problem there are efficient solutions. In this extended abstract, we show polylogrithmic time algorithm for this problem.
Research supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. OGP0046373.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. Apostolico, M.J. Atallah, L.L. Larmore and S. Mcfaddin, ‘Efficient parallel algorithms for string editing and related problems', SIAM J. Comput., vol. 19, no. 5, pp. 968–988, 1990
S. Y. Lu, “A tree-to-tree distance and its application to cluster analysis”, IEEE Tracas. PAMI, vol. 1, pp.219–224, 1979
G. M. Landau and U. Vishkin, ‘Fast parallel and serial approximate string matching', J. Algorithms, vol. 10, pp.157–169, 1989
S. M. Selkow, ‘The tree-to-tree editing problem', Information Processing Letters, no. 6, 184–186, 1977
B. Shapiro, An algorithm for comparing multiple RNA secondary structures, Comput. Appl. Biosci., pp. 387–393, 1988
B. Shapiro and K. Zhang, ‘Comparing multiple RNA secondary structures using tree comparisons’ Comput. Appl. Biosci. vol. 6, no. 4, pp.309–318, 1990
D. Shasha and K. Zhang, ‘Fast algorithms for the unit cost edit distance between trees', J. of Algorithms, vol. 11, pp. 581–621, 1990
K. C. Tai, ‘The tree-to-tree correction problem', J. ACM, vol. 26, pp.422–433, 1979
K. Zhang, ‘A new editing based distance between unordered labeled trees', In A. Apostolico, M. Crochemore, Z. Galil, and U. Manber, editors, Combinatorial Pattern Matching, Lecture Notes in Computer Science, 684, pp. 254–265. Springer-Verlag, 1993; journal version is to appear in Algorithmica.
K. Zhang, ‘Efficient parallel algorithms for tree editing problems', Proceedings of the Seventh Symposium on Combinatorial Pattern Matching
K. Zhang, J. Wang and D. Shasha, ‘On the editing distance between undirected acyclic graphs', Proceedings of the Sixth Symposium on Combinatorial Pattern Matching, Helsinki, Finland, July 1995. Springer-Verlag's Lecture Notes in Computer Science 937, pp 395–407.
K. Zhang and D. Shasha, ‘Simple fast algorithms for the editing distance between trees and related problems', SIAM J. Computing vol. 18, no. 6, pp. 1245–1262, 1989
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, K. (1998). Efficient parallel algorithm for the editing distance between ordered trees. In: Farach-Colton, M. (eds) Combinatorial Pattern Matching. CPM 1998. Lecture Notes in Computer Science, vol 1448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030782
Download citation
DOI: https://doi.org/10.1007/BFb0030782
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64739-3
Online ISBN: 978-3-540-69054-2
eBook Packages: Springer Book Archive