Let U = {1, . . . , n} be a collection of n elements and S = {S1, . . . , Sm} be a collection of m subsets of U (i.e., Sj U for j = 1, . . . , m) such that U = m j=1Sj . The set Sj is associated with a non-negative cost cj , for j = 1, . . . , m