I read slide about top-k algorithms which are Fagin Algorithm (FA), Threshold Algorithm (TA) and No random access algorithm (NRA). Those algorithms are good because we do not need to see all values, we just need to set a threshold or compute lower bound and upper bound.
Slide = http://alumni.cs.ucr.edu/~skulhari/Top-k-Query.pdf
Now, I have large of data points and I want to get the top-k points (subset) which diversity maximum, means that the distances among points in the top-k (subset) are maximum. I know that this problem is NP-Hard. The algorithm such as Brute force is not feasible for this case due to the dataset is large.
In here, I just want to know, is it possible to get subset/top-k points without computing all distances among all pair points like in FA/TA/NRA algorithm?