Dynamic programming based RNA pseudoknot alignment

Pseudoknots are certain structural motifs of RNA molecules. In this thesis we consider the problem of RNA pseudoknot alignment. Most current approaches either discard pseudoknots in order to be efficient or rely on heuristics generating only approximate solutions. This work focuses on dynamic programming based alignment methods and proposes two new approaches for an exact solution of the alignment problem in the presence of pseudoknot structures. The first approach is able to handle arbitrary pseudoknots, however, does not guarantee a polynomial runtime for all instances, due to the NP-hardness of the problem. Nevertheless, an analysis in terms of parameterized complexity shows that the algorithm is fixed parameter tractable for a parameter that is small in practice. The second approach is a general scheme for the alignment of restricted classes of pseudoknots in polynomial time. It is motivated by existing RNA pseudoknot prediction algorithms. We show how to embed seven of those algorithms in a common scheme and present an analogous scheme for the alignment problem, which yields for each of the structure prediction algorithms a corresponding alignment algorithm. The alignment algorithms handle the same class of pseudoknots as the corresponding prediction algorithms and the time and space complexity is only increased by a linear factor, compared to the respective prediction algorithm. Both approaches have been implemented to evaluate their applicability in practice.