Edit distance between two RNA structures
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
The Longest Common Subsequence Problem for Sequences with Nested Arc Annotations
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Algorithms and complexity for annotated sequence analysis
Algorithms and complexity for annotated sequence analysis
How to compare arc-annotated sequences: the alignment hierarchy
SPIRE'06 Proceedings of the 13th international conference on String Processing and Information Retrieval
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)
A propagator for maximum weight string alignment with arbitrary pairwise dependencies
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A new algorithm for aligning nested arc-annotated sequences under arbitrary weight schemes
Theoretical Computer Science
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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In molecular biology, RNA structure comparison is of great interest to help solving problems as different as phylogeny reconstruction, prediction of molecule folding and identification of a function common to a set of molecules. Lin et al. [6] proposed to define a similarity criterion between RNA structures using a concept of edit distance ; they named the corresponding problem Edit. Recently, Blin et al. [3] showed that another problem, the Longest ARC-Preserving Common Subsequence problem (or LAPCS), is in fact a subproblem of Edit. This relationship between those two problems induces the hardness of what was the last open case for the Edit problem, Edit(NESTED, NESTED), which corresponds to computing the edit distance between two secondary structures without pseudoknots. Nevertheless, LAPCS is a very restricted subproblem of Edit: in particular, it corresponds to a given system of editing costs, whose biological relevance can be discussed ; hence, giving a more precise categorization of the computational complexity of the Edit problem remains of interest. In this paper, we answer this question by showing that EDIT(NESTED, NESTED) is NP-complete for a large class of instances, not overlapping with the ones used in the proof for LAPCS, and which represent more biologically relevant cost systems.