Impact of the Energy Model on the Complexity of RNA Folding with Pseudoknots

  • Saad Sheikh
  • Rolf Backofen
  • Yann Ponty
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7354)


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 Θ(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 work, we consider an intermediate model, called the stacking-pairs energy model. We extend a result by Lyngsø, showing that RNA folding with PK is NP-Hard within a large class of parametrization for the model. We also show the approximability of the problem, by giving a practical Θ(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.


RNA folding General pseudoknots Hardness Inapproximability 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Saad Sheikh
    • 1
    • 4
  • Rolf Backofen
    • 2
  • Yann Ponty
    • 3
    • 4
  1. 1.University of FloridaGainesvilleUSA
  2. 2.Albert Ludwigs UniversityFreiburgGermany
  3. 3.Ecole Polytechnique, CNRS UMR 7161PalaiseauFrance
  4. 4.AMIB Team-Project, INRIASaclayFrance

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