I have a set *S* of real numbers, and I would like to create a new set *R* with exactly n real numbers (not necessarily from the set) that represent it best.

What I mean by best?

Well, I have query that asks for given point what is the closest point from S to that point, and when I ask same thing for set R I would like to have best fit to the real answers.

To be specific, how do I minimize the Hausdoff distance between

SandR?

I hope I've been clear enough in what i want. I've heard of mathoverflow, so I said to myself why wouldn't I ask for help there.

Thank you in advance.

(**Edited** in light of the comments below.)

`$|\operatorname{dist}(x,R)-\operatorname{dist}(x,S)|\le h$`

, and $h$ is the smallest such number. So the question should perhaps be about minimizing Hausdorff distance. – Harald Hanche-Olsen Feb 19 '10 at 17:02