Speedup of RNA Pseudoknotted Secondary Structure Recurrence Computation with the Four-Russians Method
While secondary pseudoknotted structure prediction is computationally challenging, such structures appear to play biologically important roles in both cells and viral RNA . Restricting the class of possible structures and then finding the optimal structure for that restricted class is a common method employed to deal with the computational complexity.
We derive a practical and worst-case speedup algorithm using the Four-Russians method for the O(n 6) time Rivas&Eddy Algorithm  describing the broadest set of structures. Fast R&E algorithm finds the optimal Rivas&Eddy fold in O(n 6/q)-time, where q ≥ log(n).
Because the solution matrix produced by Fast R&E algorithm is identical to the one produced by the original Rivas&Eddy algorithm, the contribution of the algorithm lies not only in its stand alone practicality but also in its ability to be implemented alongside heuristic speedups, leading to even greater reductions in time. Our approach is the first to achieve a Ω(log(n)) time speedup without reducing the set of possible Rivas&Eddy pseudoknotted structures. The analysis presented here of the original algorithm could be used to improve other pseudoknot algorithms with similar recurrences.
KeywordsIndex Point Secondary Struc Pseudoknotted Structure Compute Matrix Multiple Structural Alignment
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- 17.Deogun, J.S., Donts, R., Komina, O., Ma, F.: RNA secondary structure prediction with simple pseudoknots. In: Chen, Y.-P.P. (ed.) APBC. CRPIT, vol. 29, pp. 239–246. Australian Computer Society (2004)Google Scholar
- 23.Williams, R.: Matrix-vector multiplication in sub-quadratic time (some preprocessing required). In: Bansal, N., Pruhs, K., Stein, C. (eds.) SODA, pp. 995–1001. SIAM (2007)Google Scholar