Simple fast algorithms for the editing distance between trees and related problems
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Computing the similarity of two sequences with nested arc annotations
Theoretical Computer Science
Pattern matching for arc-annotated sequences
ACM Transactions on Algorithms (TALG)
Comparing RNA structures: towards an intermediate model between the edit and the LAPCS problems
BSB'07 Proceedings of the 2nd Brazilian conference on Advances in bioinformatics and computational biology
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
An edit distance between RNA stem-loops
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
Extending the hardness of RNA secondary structure comparison
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
The longest common subsequence problem with crossing-free arc-annotated sequences
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
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Arc-annotated sequences are useful for representing structural information of RNAs and have been extensively used for comparing RNA structures in both terms of sequence and structural similarities. Among the many paradigms referring to arc-annotated sequences and RNA structures comparison (see [2] for more details), the most important one is the general edit distance. The problem of computing an edit distance between two non-crossing arc-annotated sequences was introduced in [5]. The introduced model uses edit operations that involve either single letters or pairs of letters (never considered separately) and is solvable in polynomial-time [12]. To account for other possible RNA structural evolutionary events, new edit operations, allowing to consider either silmutaneously or separately letters of a pair were introduced in [9]; unfortunately at the cost of computational tractability. It has been proved that comparing two RNA secondary structures using a full set of biologically relevant edit operations is NP-complete. Nevertheless, in [8], the authors have used a strong combinatorial restriction in order to compare two RNA stem-loops with a full set of biologically relevant edit operations; which have allowed them to design a polynomial-time and space algorithm for comparing general secondary RNA structures. In this paper we will prove theoretically that comparing two RNA structures using a full set of biologically relevant edit operations cannot be done without strong combinatorial restrictions.