Predicting the folding of an RNA sequence, while allowing general pseudoknots (PK), consists in finding a minimal free-energy matching of its /n/ positions.
Assuming independently contributing base-pairs, the problem can be solved in O(/n/^3 )-time using a variant of the maximal weighted matching.
By contrast, the problem was previously proven NP-Hard in the more realistic nearest-neighbor energy model.
In this joint work with Rolf Backofen (Uni Freiburg, Germany) and Saad Sheikh (University of Florida, USA), we consider an intermediate model, called the stacking-pairs energy model.
We extend a result by Lyngso, showing that RNA folding with PK is NP-Hard within a large class of parametrization of the model. We also show the approximability of the problem, by giving a practical O(/n/^3 ) algorithm that achieves at least a 5-approximation for any parametrization of the stacking model. This contrasts nicely with the nearest-neighbor version of the problem, which we prove cannot be approximated within any positive ratio, unless P=NP.