A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
On finding minimal, maximal, and consistent sequences over a binary alphabet
Theoretical Computer Science
TAL recognition in O(M(n2)) time
Journal of Computer and System Sciences
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
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It is well known that a basic version (i.e., maximizing the number of base-pairs) of the RNA secondary structure prediction problem can be solved in O(n3) time by using simple dynamic programming procedures. For this problem, an O(n3(log log n)1/2/(log n)1/2) time exact algorithm and an O(n2.776 + (1/ε)O(1)) time approximation algorithm which has guaranteed approximation ratio 1-ε for any positive constant ε are also known. Moreover, when two RNA sequences are given, there is an O(n6) time exact algorithm which can optimize structure and alignments. In this paper, we show an O(n5) time approximation algorithm for optimizing structure and alignments of two RNA sequences with assuming that the optimal number of base-pairs is more than O(n0.75). We also show that the problem to optimize structure and alignments for given N sequences is NP-hard and introduce a constant-factor approximation algorithm.