Creating minimum number of polygons that surround multiple points in ArcGIS Desktop?

Question

I have around 300 points randomly distributed (some near to each other, some far from each other) on a map.

I want to create a layer that contains multiple circle polygons of 800 metres diameter such that these polygons are able to encompass all the above 300 points. And that the number of such polygons are as minimal as possible in achieving the above.

Initially, I tried using the buffer tool but realized this is not the correct one. I am using ArcGIS 10.3 Desktop version

Answer 1

I have not tested this but I think what I would try is:

1. Keep a copy of your original point feature class
2. Run Point Distance on your feature class so that you can determine the point which has the most other points within 400 metres of it.
3. Delete that point and repeat step 2, and keep repeating until you have no points with any points within 400 metres.
4. Buffer those points by 400 metres and draw the original points on the buffer polygons.

If you see any points outside the buffers reassess this method.

Point Distance requires an Advanced license which you do not have, but there is an available workaround for Performing Point Distance analysis using Basic level license of ArcGIS for Desktop?