An optimal decomposition algorithm for tree edit distance
The edit distance between two ordered rooted trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this paper, we present a worst-case O(n 3)-time algorithm for this problem, improving the previous best O(n3 log n)-time algorithm [7]. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems, together with a deeper understanding of the previous algorithms for the problem. We prove the optimality of our algorithm among the family of decomposition strategy algorithms-which also includes the previous fastest algorithms-by tightening the known lower bound of Q(n2 log2 n) [4] to Ωn 3), matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds of ⊖(nm2(1 + log m/n)) when the two trees have sizes m and n where m < n. © Springer-Verlag Berlin Heidelberg 2007.
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- Artificial Intelligence & Image Processing
- 46 Information and computing sciences
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Published In
DOI
EISSN
ISSN
Publication Date
Volume
Start / End Page
Related Subject Headings
- Artificial Intelligence & Image Processing
- 46 Information and computing sciences