Hi Stavros:
I think these minimal sets are called 'atoms'.
I believe that there are 'fast' (< quadratic) algorithms for this problem.
At 08:11 AM 4/8/2013, Stavros Macrakis wrote:
>Given a set of sets S, what is the minimal set of disjoint sets D such that each of the original sets is a union of elements of D?
>
>For example, if S = { {a,b,c,d,e}, {a,c}, {c,f,g} }, then D = { {a}, {c}, {f, g}, {b,d,e} }.
>
>What is the name of this problem?
>
>The obvious way to solve it is to calculate the full lattice of intersections and set differences, but the straightforward way of doing that seems computationally expensive. What are good algorithms for this problem?
>
> -s