On the Approximation of Shortest Common Supersequencesand Longest Common Subsequences
SIAM Journal on Computing
Finding similar regions in many strings
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
On the closest string and substring problems
Journal of the ACM (JACM)
Finding motifs in the twilight zone
Proceedings of the sixth annual international conference on Computational biology
Finding similar regions in many sequences
Journal of Computer and System Sciences - STOC 1999
Extracting Common Motifs under the Levenshtein Measure: Theory and Experimentation
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
A Polynominal Time Approximation Scheme for the Closest Substring Problem
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
Distinguishing string selection problems
Information and Computation
Algorithms for computing variants of the longest common subsequence problem
Theoretical Computer Science
A New Efficient Algorithm for Computing the Longest Common Subsequence
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Algorithms for computing variants of the longest common subsequence problem
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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The longest common subsequence problem (LCS) and the closest substring problem (CSP) are two models for the finding of common patterns in strings. The two problem have been studied extensively. The former was previously proved to be not polynomial-time approximable within ratio nδ for a constant δ. The latter was previously proved to be NP-hard and have a PTAS. In this paper, the longest common rigid subsequence problem (LCRS) is studied. LCRS shares similarity with LCS and CSP and has an important application in motif finding in biological sequences. LCRS is proved to be Max-SNP hard in this paper. An exact algorithm with quasi-polynomial average running time is also provided.