Optimum partitioning into intersections of ring families Original Research Article

Given two ring families C and D on a finite ground set V, with both ø and V ϵ C and D, consider the family of so-called intersections L = [L ⊂- V¦L = C∩D, C ϵ C, D ϵ D and C∪D = V] and let A be the incidence matrix of L. The minimum partitioning problem: “Given a vector d ϵ Zv+, minimize y1 s.t. yA = d, y ⩾ 0, y integer”, is solved by a longest path computation. The approach is polyhedral and capitalizes on previous results related to lattice matrices.