A Worst-Case and Practical Speedup for the RNA Co-folding Problem Using the Four-Russians Idea

The computational formulation for finding the optimal simultaneous alignment and fold (optimal Co-fold) of RNA sequences was first introduced by Sankoff in 1985. Since then the importance of Co-Folding has grown as conservation of structure and its relationship to function have been widely observed in RNA. For two sequences, the computation time of Sankoff's Algorithm is θ(N6). Existing literature on cofolding attempts to improve efficiency through simplifying the original problem formulation. We present here a practical and worst-case speed up using the Four-Russians method, without placing any added constraints on the types of alignments or folds allowed. Our algorithm, Fast Cofold, finds the optimal Co-fold in O(N6/ log(N2))-time, a speedup which is observed in practice. Because the solution matrix produced by our algorithm is identical to the one produced by the Sankoff algorithm, the contribution of the algorithm lays not only in its standalone practicality but also in the ability to implement it alongside heuristic speed ups leading to even greater reductions in time.

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