An Improved Context-Free Recognizer
ACM Transactions on Programming Languages and Systems (TOPLAS)
Algorithm Design
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A worst-case and practical speedup for the RNA co-folding problem using the four-Russians idea
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Reducing the worst case running times of a family of RNA and CFG problems, using Valiant's approach
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Speeding up Bayesian HMM by the four Russians method
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
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The problem of computationally predicting the secondary structure (or folding) of RNA molecules was first introduced more than thirty years ago and yet continues to be an area of active research and development. The basic RNA-folding problem of finding a maximum cardinality, non-crossing, matching of complimentary nucleotides in an RNA sequence of length n, has an O(n3)-time dynamic programming solution that is widely applied. It is known that an o(n3) worst-case time solution is possible, but the published and suggested methods are complex and have not been established to be practical. Significant practical improvements to the original dynamic programming method have been introduced, but they retain the O(n3) worst-case time bound when n is the only problem-parameter used in the bound. Surprisingly, the most widely-used, general technique to achieve a worst-case (and often practical) speed up of dynamic programming, the Four-Russians technique, has not been previously applied to the RNA-folding problem. This is perhaps due to technical issues in adapting the technique to RNA-folding. In this paper, we give a simple, complete, and practical Four-Russians algorithm for the basic RNA-folding problem, achieving a worst-case time-bound of O(n3/ log(n)). We show that this time-bound can also be obtained for richer nucleotide matching scoring-schemes, and that the method achieves consistent speed-ups in practice. The contribution is both theoretical and practical, since the basic RNA-folding problem is often solved multiple times in the inner-loop of more complex algorithms, and for long RNA molecules in the study of RNA virus genomes.