Efficient parallel algorithms for tree editing problems
The tree editing problem for input trees T1 and T2 is defined as transforming T1 into T2 by performing a series of weighted edit operations on T1 with overall minimum cost. An edit operation can be the deletion, the insertion, and the substitution. Depending on the precise definition of the edit operation, there are several edit distances between trees. This paper presents a framework for solving tree editing problems in parallel. We show polylogrithmic time algorithms under this framework.
KeywordsParallel Algorithm Edit Distance Edit Operation Maximum Weighted Match Unordered Tree
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- 1.A. Aggarwal and J. Park, ‘Notes on searching in multidimensional monotone arrays', In Proc. 29th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Washinton, DC, pp. 497–512, 1988Google Scholar
- 3.S. Y. Lu, “A tree-to-tree distance and its application to cluster analysis”, IEEE Trans. PAMI, vol. 1, pp.219–224, 1979Google Scholar
- 5.S. M. Selkow, ‘The tree-to-tree editing problem', Information Processing Letters, no. 6, 184–186, 1977Google Scholar
- 6.B. Shapiro, An algorithm for comparing multiple RNA secondary structures, Comput. Appl. Biosci., pp. 387–393, 1988Google Scholar
- 8.D. Shasha and K. Zhang, ‘Fast algorithms for the unit cost edit distance between trees', J. of Algorithms, vol. 11, pp. 581–621, 1990Google Scholar
- 9.K. C. Tai, ‘The tree-to-tree correction problem', J. ACM, vol. 26, pp.422–433, 1979Google Scholar
- 10.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.Google Scholar
- 11.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.Google Scholar
- 12.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, 1989Google Scholar