So I have a set of given locations (i.e. two-dimensional points) G, a set of wanted locations W and a natural number N. Assume |W| < N. I want to choose N elements of G such that

  1. the elements of W are somewhat covered (i.e. for each element of W there is a chosen element of G that is "nearby") and
  2. the choosen points are somewhat distributed equalently amoung the overall points from L, i.e. the overall distance between a non choosen point and its next choosen point is small.

So for 1. I guess looking for the nearest neighbor (or two nearest) is good. For 2. I think something like k-nearest-Neighbors would work, just with keeping a certain amount of centers (these from 2.) constant.

I would apprechiate your thoughts on the matter, other solutions etc. Trying not to keep my question to broad: Does this problem has a name or are there known solutions? I'm kinda missing the search words yet.

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