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
Distinguishing string selection problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs
Journal of the ACM (JACM)
Introduction to Algorithms
Efficient Computation of All Longest Common Subsequences
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
A PTAS for Distinguishing (Sub)string Selection
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
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.
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Algorithms for computing variants of the longest common subsequence problem
Theoretical Computer Science
Approximation of RNA multiple structural alignment
Journal of Discrete Algorithms
The approximability of the exemplar breakpoint distance problem
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Approximation of RNA multiple structural alignment
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Lower bounds on the approximation of the exemplar conserved interval distance problem of genomes
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
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In this paper, we present a new model for RNA multiple sequence structural alignment based on the longest common subsequence. We consider both the off-line and on-line cases. For the off-line case, i.e., when the longest common subsequence is given as a linear graph with n vertices, we first present a polynomial O(n2) time algorithm to compute its maximum nested loop. We then consider a slightly different problem – the Maximum Loop Chain problem and present a factor-2 approximation which runs in O(n2.5) time. For the on-line case, i.e., given m RNA sequences of lengths n, compute the longest common subsequence of them such that this subsequence either induces a maximum nested loop or the maximum number of matches, we present efficient algorithms using dynamic programming when m is small.