Simple fast algorithms for the editing distance between trees and related problems
SIAM Journal on Computing
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
On the editing distance between unordered labeled trees
Information Processing Letters
Some MAX SNP-hard results concerning unordered labeled trees
Information Processing Letters
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A New Measure of the Distance between Ordered Trees and its Applications
A New Measure of the Distance between Ordered Trees and its Applications
Decomposition Method for Tree Kernels
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Part II--Advances in Neural Networks
Journal of Computer Science and Technology
Schema mapping with quality assurance for data integration
APWeb'11 Proceedings of the 13th Asia-Pacific web conference on Web technologies and applications
Dynamic programming algorithms for efficiently computing cosegmentations between biological images
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
Matchmaking OWL-S processes: an approach based on path signatures
Proceedings of the International Conference on Management of Emergent Digital EcoSystems
A theoretical analysis of alignment and edit problems for trees
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
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One of the most important problem in computational biology is the tree editing problem which is to determine the edit distance between two rooted labeled trees. It has been shown to have significant applications in both RNA secondary structures and evolutionary trees. Another viewpoint of considering this problem is to find an edit mapping with the minimum cost. By restricting the type of mapping, Zhang [7,8] and Richter [5] independently introduced the constrained edit distance and the structure respecting distance, respectively. They are, in fact, the same concept. In this paper, we define a new measure of the edit distance between two rooted labeled trees, called less-constrained edit distance, by relaxing the restriction of constrained edit mapping. Then we study the algorithmic complexities of computing the less-constrained edit distance between two rooted labeled trees. For unordered labeled trees, we show that this problem is NP-complete and even has no absolute approximation algorithm unless P = NP, which also implies that it is impossible to have a PTAS for the problem. For ordered labeled trees, we give a polynomial-time algorithm to solve the problem.