Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Embedding graphs in books: a layout problem with applications to VLSI design
SIAM Journal on Algebraic and Discrete Methods
Embedding planar graphs in four pages
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
A polyhedral approach to RNA sequence structure alignment
RECOMB '98 Proceedings of the second annual international conference on Computational molecular biology
Efficient approximation schemes for maximization problems on K3,3-free of K5-free graphs
Journal of Algorithms
Efficient algorithms for Petersen's matching theorem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
The String-to-String Correction Problem
Journal of the ACM (JACM)
Near optimal multiple alignment within a band in polynomial time
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Algorithmic Aspects of Protein Structure Similarity
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The longest common subsequence problem.
The longest common subsequence problem.
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)
A remark on the subsequence problem for arc-annotated sequences with pairwise nested arcs
Information Processing Letters
Algorithms for computing variants of the longest common subsequence problem
Theoretical Computer Science
Fast Arc-Annotated Subsequence Matching in Linear Space
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A metric for rooted trees with unlabeled vertices based on nested parentheses
Theoretical Computer Science
A new algorithm for aligning nested arc-annotated sequences under arbitrary weight schemes
Theoretical Computer Science
Parameterized complexity of the arc-preserving subsequence problem
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Approximation of RNA multiple structural alignment
Journal of Discrete Algorithms
Approximation of RNA multiple structural alignment
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
How to compare arc-annotated sequences: the alignment hierarchy
SPIRE'06 Proceedings of the 13th international conference on String Processing and Information Retrieval
Fixed-parameter algorithms for protein similarity search under mRnA structure constraints
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Local gapped subforest alignment and its application in finding RNA structural motifs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Local structural alignment of RNA with affine gap model
ISBRA'10 Proceedings of the 6th international conference on Bioinformatics Research and Applications
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Local exact pattern matching for non-fixed RNA structures
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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 in representing the structural information of RNA and protein sequences. The LONGEST ARc-PRESERVING COMMON SUBSEQUENCE (LAPCS) Problem has been introduced in Evans (Algorithms and complexity for annotated sequence analysis, Ph.D. Thesis, University of Victoria, 1999) as a framework for studying the similarity of arc-annotated sequences. Several algorithmic and complexity results on the LAPCS problem have been presented in Evans (1999) and Jiang et al. (in: Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching (CPM 2000), Lecture Note in Computer Science, Vol. 1848, 2000, pp. 154-165). In this paper, we continue this line of research and present new algorithmic and complexity results on the LAPCS problem restricted to two nested arc-annotated sequences, denoted as LAPCS(NESTED, NESTED). The restricted problem is perhaps the most interesting variant of the LAPCS problem and has important applications in the comparison of RNA secondary structures. Particularly, we prove that LAPCS(NESTED, NESTED) is NP-hard, which answers an open question in Evans (1999). We then present a polynomial-time approximation scheme for LAPCS(NESTED, NESTED) with an additional c-diagonal restriction. An interesting special case, UNARY LAPCS(NESTED, NESTEO), is also investigated, for which we show the NP-hardness and present a better approximation algorithm than the one for general LAPCS(NESTED, NESTED).