On the approximation of optimal structures for RNA-RNA interaction.

The interaction of two RNA molecules is a common mechanism for many biological processes. Small interfering RNAs represent a simple example of such an interaction. But other more elaborate instances of RNA-RNA interaction exist. Therefore, algorithms that predict the structure of the RNA complex thus formed are of great interest. Most of the proposed algorithms are based on dynamic programming. RNA-RNA interaction is generally NP-complete; therefore, these algorithms (and other polynomial time algorithms for that matter) are not expected to produce optimal structures. Our goal is to characterize this suboptimality. We demonstrate the existence of constant factor approximation algorithms that are based on dynamic programming. In particular, we describe 1/2 and 2/3 factor approximation algorithms. We define an entangler and prove that 2/3 is a theoretical upper bound on the approximation factor of algorithms that produce entangler-free solutions, e.g., the mentioned dynamic programming algorithms.