string,pattern-matching,approximate

You might want to read about Levenshtein distance. http://en.wikipedia.org/wiki/Levenshtein_distance...

python,vector,linear-algebra,mathematical-optimization,approximate

I agree that in general this is a pretty tough optimization problem, especially at the scale you're describing. Each objective function evaluation requires O(nm + n^2) work for n points of dimension m -- O(nm) to compute distances from each point to the new point and O(n^2) to compute the...