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(n 3 ) time algorithms were known. For both problems, this paper shows slightly improved O(n 3 (log logn) 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(n 2.776 + (1/∈) O(1) ) time approximation algorithm for the former problem and an O(n 2.976 log n + (1/∈) O(1) ) time approximation algorithm for the latter problem, each of which has a guaranteed approximation ratio I - ∈ 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 algonthm is obtained from a non-trivial modification of the well-known O(n 3 ) 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.