Algorithm to find minimal elements needed to uniquely identify a collection of those elements?

If the order is not important, I would sort all Lists (Collections).

This is an easy problem to solve. You have one multiset (collection 1) (it is a "multiset" because the same element can occur multiple times), and then a number of other multisets (collections 2..N), and you want to find a minimum-size subset of collection 1 that does not occur in any of the other collections (2..N).

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