Problem Detail: 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.
Asked By : Jose M Vidal
Answered By : Vor
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.
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