Detection of circles (ellipses) in 2D point cloud
The best ideas that exactly tries to solve this problem is Hough Transform . 

Basically, the signal in hough space will be r, x, y co-ordinates. Here r
 stands for radius and x,y stands for center. Every points may belong to one or many circles. So in the Hough plane go through all possible circles where this point could belong to and just do a +1. This is not a search, just collection. 

Now, if a real circle exists, so many points will add and the score of such a r, x, y will be much higher than all others. Selecting such a point will allow you pick the right circles. 

Here is a classical paper way back in 1971 (before i was born!) that invented this concept. 


USE OF THE HOUGH TRASFORMTION  TO DETECT LINES AND CURVES IN PICTURES 
By:  Richard O. Duda, Peter E. Hart 
Tech report Artificial Intelligence Cente April 1971. 


For Tutorial i would suggest references below:


HIPR2 -Link 
Amos storkey
IDL Reference 


Specifically for circle detection, you can refer to this below:


AI Shack 
Tech Report from Chicago Univ. 
Lecture Notes from Rochester Institute


These methods is very efficient, and very computer friendly.