[joker3]

There's no matching process at the beginning of medical school, but there is for assigning med school graduates to residencies. This variant of the problem is NP-hard, so there's no exact solution, but matching still works pretty well. https://web.stanford.edu/~alroth/papers/rothperansonaer.PDF has all the details.

[QML]

When you are referring to this "variant", are you referring to maximal matching, or bipartite matching when the number of people and schools don't equal?

[andreareina]

Not the parent, but I think they refer to the fact that with admissions, matches are permanent (once a student accepts a school's offer, said offer can't be rescinded), while Gale-Shapely requires provisional pairings until all the rounds have been gone through and a final result is available.

[joker3]

The issue is that couples want to be placed together. That makes everything trickier than if people just placed independently.