Minimal elements of a poset

Hi,

I have a set of finite sets over the fixed domain {1...n}, eg { {1}, {1,2}, {1,3}, {2} }. In the algorithm I am implementing, the most time-consuming step is to compute all minimal elements wrt to the subset relation. My current implementation uses a quadratic algorithm together with some heuristics, but for large sets, this becomes very inefficient.

Does anybody know any efficient algorithm (or a proven lower bound for complexity) for this problem?
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