Sparsification in Algebraic Dynamic Programming

Sparsification is a technique to speed up dynamic programming algorithms which has been successfully applied to RNA structure prediction, RNA-RNA-interaction prediction, simultaneous alignment and folding, and pseudoknot prediction. So far, sparsification has been more a collection of loosely related examples and no general, well understood theory. In this work we propose a general theory to describe and implement sparsification in dynamic programming algorithms. The approach is formalized as an extension of Algebraic Dynamic Programming (ADP) which makes it applicable to a variety of algorithms and scoring schemes. In particular, this is the first approach that shows how to sparsify algorithms with scoring schemes that go beyond simple minimization or maximization, like enumeration of suboptimal solutions and approximation of the partition function. As an example, we show how to sparsify different variants of RNA structure prediction algorithms.