Given a distance matrix for 50,000 points, how do I select $N$ points so that the sum of all distances between the $N$ points is maximized? $N$ could be as high as 100.
To calculate the sum of distances for all sets of $N$ points would be exponential, which would not scale to 50,000 points.
What is the fastest algorithm that you would know? And also, does this problem have a name? If so, I could do more reading about it.
Thanks very much for your feedback.