I am trying to solve a sub problem of set cover. For example, the U={ (1,2,3), (4,3), (5,3), (1,2), (4) } I want to find the minimum number of sets that cover all the elements in U, however with a constraint that the solution set should not have overlapping element between them. In this case, a subset {(5,3), (1,2), (4)} is a solution, but the subset {(1,2,3), (4,3), (5,3)} is not a solution.
Has anyone already studied this before? What is it called in the literature? Any algorithm suggested?
