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
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
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
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
An edit distance between RNA stem-loops
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
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An arc-annotated sequence is a sequence, over a given alphabet, with additional structure described by a set of arcs, each arc joining a pair of positions in the sequence. As a natural extension of the longest common subsequence problem, Evans introduced the Longest Arc-Preserving Common Subsequence (LAPCS) problem as a framework for studying the similarity of arc-annotated sequences. This problem has been studied extensively in the literature due to its potential application for RNA structure comparison, but also because it has a compact definition. In this paper, we focus on the nested case where no two arcs are allowed to cross because it is widely considered the most important variant in practice. Our contributions are three folds: (i) we revisit the nice NP-hardness proof of Lin et al. for LAPCS(Nested, Nested), (ii) we improve the running time of the FPT algorithm of Alber et al. from $O(3.31^{k_1 + k_2} n)$ to $O(3^{k_1 + k_2} n)$, where resp. k1 and k2 deletions from resp. the first and second sequence are needed to obtain an arc-preserving common subsequence, and (iii) we show that LAPCS(Stem, Stem) is NP-complete for constant alphabet size.