[ REQ 5459]: Interesting Problem?

["Arnie Cutler" <cutler>]

	My son is in graduate school at U of Washington in Seattle.   
He is currently working on a problem from a computational point of  
view and I am wondering if we might have software which would  
illuminate the problem from a visual perspective.  The problem is:

Given a set of n points with n large and all subsets m of those  
points where m is small relative to n, select the subset of size m  
which maximizes the total distance between the m points.  E.G. If you  
had a set of 1000 points and a subset of size 5, find the subset of  
five points such that the sum of the distances from 1 to 2, 1 to 3, 1  
to 4, 1 to 5, 2 to 3, 2 to 4, 2 to 5, 3 to 4, 3 to 5, 4 to 5 is  
maximized.  


Arnie