We are interested in the minimality problem in the context of combinations of qualitative constraint networks (such as temporal sequences, multiscale networks, and loose integrations). For this, we generalize the minimality problem of the classical framework. This brings us to two distinct and complementary notions of minimality. We then study the complexity of the generalized minimality problem. In addition, we identify conditions ensuring that the algebraic closure computes the generalized minimal network. Based on this result, we prove that the topological temporal sequences of constant-size regions over the subclass SRCC8 check this property. This contrasts with the sequences of convex relations that do not verify it. Moreover, we study the complexity of the satisfiability decision of relations as well as the enumeration of satisfiable basic relations.