Separation of partition inequalities with terminals

Given a graph with n nodes each of them having labels equal either to 1 or 2 (a node with label 2 is called a terminal), we consider the (1,2)-survivable network design problem and more precisely, the separation problem for the partition inequalities. We show that this separation problem reduces to a sequence of submodular flow problems. Based on an algorithm developed by Fujishige and Zhang the problem is reduced to a sequence of O(n⁴) minimum cut problems.