Simple fast algorithms for the editing distance between trees and related problems
SIAM Journal on Computing
Alignment of trees: an alternative to tree edit
Theoretical Computer Science
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Computing similarity between RNA structures
Theoretical Computer Science
The longest common subsequence problem for sequences with nested arc annotations
Journal of Computer and System Sciences - Computational biology 2002
Algorithms and complexity for annotated sequence analysis
Algorithms and complexity for annotated sequence analysis
Local Similarity in RNA Secondary Structures
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Local similarity between quotiented ordered trees
Journal of Discrete Algorithms
Fast detection of common sequence structure patterns in RNAs
Journal of Discrete Algorithms
RNA pseudoknot structures with arc-length ≥3 and stack-length ≥σ
Discrete Applied Mathematics
How to compare arc-annotated sequences: the alignment hierarchy
SPIRE'06 Proceedings of the 13th international conference on String Processing and Information Retrieval
An edit distance between RNA stem-loops
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
An optimal decomposition algorithm for tree edit distance
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Extending the hardness of RNA secondary structure comparison
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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In this paper, we propose a new algorithm for the alignment of nested arc-annotated sequences, having applications in the comparison of RNA secondary structures without pseudo-knots. We use a general edit distance model between arc-annotated sequences, that considers classical sequences of edit operations and structural edit operations on arcs. In this model, the general edit distance problem under a non-constrained weight scheme, is NP-hard. Recently, a hierarchy of arc-annotated sequence alignment problems that highlights less general, but tractable, problems was introduced. We refine this hierarchy of alignment problems and extend the class of tractable alignment problems. Up to date, the alignment problem we solve is the most general one that is known to be tractable in the considered edit distance model and under arbitrary weight schemes. This algorithm is efficient, as its asymptotic time and space complexities are the same as the complexities of the best previously published algorithm.