Problem 61: RNA Folding

Suggested by	Qin Zhang
Source	Bertinoro 2014
Short link	https://sublinear.info/61

An RNA sequence is a string of letters from the alphabet {A, C, G, U}, where A-U and C-G form pairings. A set of pairings in such a string is said to be non-crossing if there are no pairs of the form $(i, j)$ and $(k, l)$, where $i < k < j < l$.

A maximum non-crossing matching is a pairing of A-U and C-G of maximum cardinality that is non-crossing. Given a string, such a matching can be computed in $O(n^2)$ space and $O(n^3)$ time via dynamic programming [Eddy-04].

Note that there is a trivial 2-approximation to the optimal matching. Find the optimal matchings on the A, U and C, G subsequences, and take the larger one. This can be computed in a stream.

Is there a streaming algorithm that yields a factor better than 2 (in a small number of passes)?