RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Pattern Matching for Arc-Annotated Sequences
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Pattern Matching Problems over 2-Interval Sets
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Computing Similarity between RNA Structures
CPM '99 Proceedings of the 10th Annual Symposium on Combinatorial Pattern Matching
Finding Common Subsequences with Arcs and Pseudoknots
CPM '99 Proceedings of the 10th Annual Symposium on Combinatorial Pattern Matching
The Longest Common Subsequence Problem for Arc-Annotated Sequences
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
Algorithmic Aspects of Protein Structure Similarity
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Algorithms and complexity for annotated sequence analysis
Algorithms and complexity for annotated sequence analysis
On the computational complexity of 2-interval pattern matching problems
Theoretical Computer Science
Computing the similarity of two sequences with nested arc annotations
Theoretical Computer Science
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
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In molecular biology, RNA structure comparison and motif search are of great interest for solving major problems such as phylogeny reconstruction, prediction of molecule folding and identification of common functions. RNA structures can be represented by arc-annotated sequences (primary sequence along with arc annotations), and this paper mainly focuses on the so-called arc-preserving subsequence (APS) problem where, given two arc-annotated sequences (S,P) and (T,Q), we are asking whether (T, Q) can be obtained from (S, P) by deleting some of its bases (together with their incident arcs, if any). In previous studies, this problem has been naturally divided into subproblems reflecting the intrinsic complexity of the arc structures. We show that APS(Crossing, Plain) is NP-complete, thereby answering an open problem posed in. Furthermore, to get more insight into where the actual border between the polynomial and the NP-complete cases lies, we refine the classical subproblems of the APS problem in much the same way as in and prove that both APS $(\{\sqsubset, \between\}, \emptyset)$ and APS $(\{NP-complete. We end this paper by giving some new positive results, namely showing that APS $(\{\between\}, \emptyset)$ and APS( $(\{\between\}, \{\between\})$ are polynomial time.