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
Pattern Matching for Arc-Annotated Sequences
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Extending the hardness of RNA secondary structure comparison
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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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 [11] as a framework for studying the similarity of arc-annotated sequences. Several algorithmic and complexity results on the LAPCS problem have been presented in [11,17]. 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 and tertiary structures. Particularly, we prove that LAPCS(NESTED, NESTED) is NP-hard, which answers an open question in [11]. 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, NESTED), is also investigated.