A polyhedral approach to RNA sequence structure alignment
RECOMB '98 Proceedings of the second annual international conference on Computational molecular biology
Computing similarity between RNA strings
Computing similarity between RNA strings
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
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
Fixed Parameter Tractable Alignment of RNA Structures Including Arbitrary Pseudoknots
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Lifting Prediction to Alignment of RNA Pseudoknots
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Parameterized complexity of the arc-preserving subsequence problem
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Finding common RNA pseudoknot structures in polynomial time
Journal of Discrete Algorithms
Finding common RNA pseudoknot structures in polynomial time
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Faster pattern matching algorithm for arc-annotated sequences
Proceedings of the 2005 international conference on Federation over the Web
Improved algorithms for largest cardinality 2-interval pattern problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Multiple structural RNA alignment with lagrangian relaxation
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Structural alignment of two RNA sequences with lagrangian relaxation
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Local gapped subforest alignment and its application in finding RNA structural motifs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
What makes the arc-preserving subsequence problem hard?
Transactions on Computational Systems Biology II
A multiple graph layers model with application to RNA secondary structures comparison
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
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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This paper examines the complexity of comparing sequences that have arcs linking symbol pairs. Such arc-annotated sequences can represent molecular sequences with bonds between bases, such as RNA sequences. Crossing arcs that can represent sequence pseudoknots are included. The problem of finding the longest common subsequence, on which pairwise sequence comparison algorithms are frequently based, is modified to require common subsequences to preserve the arcs induced by the selected symbol positions. This problem is then analyzed using classical and parameterized complexity. It is shown to be NP-complete, and alsoW[1]-complete when parameterized by desired length of common subsequence. If it is parameterized instead by arc cutwidth k, however, it becomes fixed-parameter tractable, and usable for sequences with arc structures of limited cutwidth. An algorithm is given that runs in time ∈ O(9knm).