Ask HN: Is optimal algo for determining global uniqueness a solved problem?

If given n groups of relatively unique vector elements (meaning that all the vectors in that group pass some kind of "uniqueness threshold", like distance from each other in 3D space), what is the fastest/optimal algorithm to determine the globally unique point set? The "uniqueness threshold" is applied equally.

If the largest possible number of globally unique points is the sum of elements in the groups somehow I feel like this would be the longest computation case?

Wondering if this is somehow an embarrassingly parallel problem that I shouldn't be missing.

I need to solve this problem for a project I am working on and I wanted to quickly check if this was some known easy/impossible problem that I should already know about.