Let universe be the union of all elements in all the sets in sets. Selects a subset of sets so that their union equals universe, i.e. a cover as specified by covered. The returned cover is in general neither minimal nor unique.

Implements the standard greedy algorithm for set cover with the following optimization:

• Do not re-insert empty sets into the priority queue
• Do not update the priority queue immediately when a newly covered element is removed from the other sets. Instead, update the priority queue only when it would have been the updated set's turn without the updates. This saves unnecessary priority queue operations as a set may be updated multiple times before it would be its turn. This is normally not done in the greedy algorithms that use a bucket priority queue because bucket operations are constant-time. We however use a heap priority queue from the standard library, whose operations are logarithmic.