Difference between revisions of "Open Problems:61"
| Line 7: | Line 7: | ||
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. | 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 n^2 space and n^3 time via dynamic programming {{cite|Eddy-04}}. | + | 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 {{cite|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. | 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)? | Is there a streaming algorithm that yields a factor better than 2 (in a small number of passes)? | ||
Revision as of 12:07, 1 June 2014
| 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)?
