Computational geometry: an introduction
Computational geometry: an introduction
Tree graphs of RNA secondary structures and their comparisons
Computers and Biomedical Research
Simple fast algorithms for the editing distance between trees and related problems
SIAM Journal on Computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
The Tree-to-Tree Correction Problem
Journal of the ACM (JACM)
A Fast Algorithm for Optimal Alignment between Similar Ordered Trees
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
Alignment of Trees - An Alternative to Tree Edit
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
New data structures for orthogonal range searching
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Maximum agreement subtree in a set of evolutionary trees-metrics and efficient algorithms
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Comparing similar ordered trees in linear-time
Journal of Discrete Algorithms
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We present a fast algorithm for optimal alignment between two similar ordered trees with node labels. Let S and T be two such trees with |S| and |T| nodes, respectively. If there exists an optimal alignment between S and T which uses at most d blank symbols and d is known in advance, it can be constructed in O(n log n·(maxdeg)^3·d^2) time, where n=max{|S|,|T|} and maxdeg is the maximum degree of all nodes in S and T. If d is not known in advance, we can construct an optimal alignment in O(n log n·(maxdeg)^3·f^2) time, where f is the difference between the highest possible score for any alignment between two trees having a total of |S|+|T| nodes and the score of an optimal alignment between S and T, if the scoring scheme satisfies some natural assumptions. In particular, if the degrees of both input trees are bounded by a constant, the running times reduce to O(n log n·d^2) and O(n log n·f^2), respectively.