Abstract
For a basic version (i.e., maximizing the number of base-pairs) of the RNA secondary structure prediction problem and the construction of a parse tree for a stochastic context-free language, O(n3) time algorithms were known. For both problems, this paper shows slightly improved O(n3(log log n)1/2/(log n)1/2) time exact algorithms, which are obtained by combining Valiant's algorithm for context-free recognition with fast funny matrix multiplication. Moreover, this paper shows an O(n2.776 + (1/∈)O(1)) time approximation algorithm for the former problem and an O(n2.976 log n + (1/∈)O(1)) time approximation algorithm for the latter problem, each of which has a guaranteed approximation ratio 1 − ∈ for any positive constant ∈, where the absolute value of the logarithm of the probability is considered as an objective value in the latter problem. The former algorithm is obtained from a non-trivial modification of the well-known O(n3) time dynamic programming algorithm, and the latter algorithm is obtained by combining Valiant's algorithm with approximate funny matrix multiplication. Several related results are shown too.
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Akutsu, T. Approximation and Exact Algorithms for RNA Secondary Structure Prediction and Recognition of Stochastic Context-free Languages. Journal of Combinatorial Optimization 3, 321–336 (1999). https://doi.org/10.1023/A:1009898029639
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DOI: https://doi.org/10.1023/A:1009898029639