Network Design Problem with Cut Constraints
In this paper, we introduce a minimum cost network design problem with a given lower bound requirement for capacity of any cut. First, we consider the subproblem including the lower bound requirement only for each fundamental cut determined by deleting edges from some spanning tree. Then, it is shown that the simplex algorithm finds an optimal solution to standard LP-relaxation of the subproblem in the linear time of the number of edges. The simplex and minimum cut algorithms are used in a Branch-and-Cut type algorithm to pick up a solution to the minimum cost network design problem.
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