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 S and R?
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.)