The K-Means based algorithm returns the optimal solution, albeit slower <br>
[[File:kmeans comparison.png]]
[[File:original algorithm.png]]
In this example, there are 16 points, with n = 4. <br>
The k-means based algorithm doesn't seem to constrain circles to have about 4 points. <br>
The previous algorithm seems to search for a point and construct a circle of the n-1 nearest points to construct a circle. <br>
This search is dependent on what point is constructed first, since all further search spaces excluded the previously constructed circle. <br>
[[File:kmeans random.png]]
[[File:original algorithm random.png]]
Here again are both is the algorithms on randomly generated points.
=Brute Force=