Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
A data structure for dynamic trees
Journal of Computer and System Sciences
Simple fast algorithms for the editing distance between trees and related problems
SIAM Journal on Computing
Fast algorithms for the unit cost editing distance between trees
Journal of Algorithms
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Pattern matching algorithms
The String-to-String Correction Problem
Journal of the ACM (JACM)
The Tree-to-Tree Correction Problem
Journal of the ACM (JACM)
A tree-edit-distance algorithm for comparing simple, closed shapes
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
New algorithm for ordered tree-to-tree correction problem
Journal of Algorithms
Algorithms on Trees and Graphs
Algorithms on Trees and Graphs
Comparing Hierarchical Data in External Memory
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
A survey on tree edit distance and related problems
Theoretical Computer Science
Analysis of tree edit distance algorithms
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
An optimal decomposition algorithm for tree edit distance
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Theoretical Computer Science
Efficient chaining of seeds in ordered trees
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Improved MAX SNP-hard results for finding an edit distance between unordered trees
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
RTED: a robust algorithm for the tree edit distance
Proceedings of the VLDB Endowment
XML information retrieval through tree edit distance and structural summaries
AIRS'11 Proceedings of the 7th Asia conference on Information Retrieval Technology
Efficient chaining of seeds in ordered trees
Journal of Discrete Algorithms
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Efficient exponential time algorithms for edit distance between unordered trees
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Theoretical Computer Science
Complexity of computing distances between geometric trees
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Style-based similarity search for office XML documents
Proceedings of the 14th International Conference on Information Integration and Web-based Applications & Services
Indexing for subtree similarity-search using edit distance
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
RWS-Diff: flexible and efficient change detection in hierarchical data
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
ADTool: security analysis with attack---defense trees
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
On the complexity of finding a largest common subtree of bounded degree
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Synthetising changes in XML documents as PULs
Proceedings of the VLDB Endowment
An Evaluation of Similarity Search Methods Blending Structures and Keywords in XML Documents
Proceedings of International Conference on Information Integration and Web-based Applications & Services
A mapping-based tree similarity algorithm and its application to ontology alignment
Knowledge-Based Systems
Natural language inference for arabic using extended tree edit distance with subtrees
Journal of Artificial Intelligence Research
Efficient exponential-time algorithms for edit distance between unordered trees
Journal of Discrete Algorithms
Journal of Combinatorial Optimization
Hi-index | 0.00 |
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 article, we present a worst-case O(n3)-time algorithm for the problem when the two trees have size n, improving the previous best O(n3 log n)-time algorithm. 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 Ω(n2 log2 n) to Ω(n3), matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds for decomposition strategy algorithms of Θ(nm2 (1 + log n/m)) when the two trees have sizes m and n and m n.