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)

Abstract

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(n3)-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(n3) 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.

Keywords

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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