Find string that minimizes the sum of the edit distances to all other strings in set I have a set of strings $S$ and I am using the edit-distance (Levenshtein) to measure the distance between all pairs.

Is there an algorithm for finding the string $x$ which minimizes the sum of the distances to all strings in $S$, that is

$\arg_x \min \sum_{s \in S} \text{edit-distance}(x,s)$

It seems like there should, but I can't find the right reference.
The problem is known as "median string problem" and it is NP-complete; some results can be found searching with Google; in particular "2-Approximation Algorithms for Median and Centre String Problems". If $x$ must be one of the points in $S$ then the problem becomes solvable in polynomial time.