Primal separation and approximation for the {0,1/2}-closure

The primal separation problem for {0,1/2}-cuts is: Given a vertex xˆ of the integer hull of a polytope P and some fractional point x^⁎∈P, does there exist a {0,1/2}-cut that is tight at xˆ and violated by x^⁎? We present two cases for which primal separation is solvable in polynomial time. Furthermore, we show that the optimization problem over the {0,1/2}-closure can be solved in polynomial time up to a factor (1+ε), for any fixed ε>0.