Algorithm to cover maximal number of points with one circle of given radius

Question

Let\'s imagine we have a plane with some points on it. We also have a circle of given radius.

I need an algorithm that determines such position of the circle that it

Answer 1

This is the "disk partial covering problem" in the literature -- that should give you a good place to start googling. Here's a paper covering one possible solution, but it is a little intense mathematically: Approximation Algorithms Design for Disk Partial Covering Problem

As a matter of fact, this falls in the area called computational geometry, which is fascinating but can be hard to get a toehold in. There's a good overview by deBerg on various algorithms related to the subject.