A suboptimal solution to a hierarchial network design problem using dynamic programming

Each arc of a network has two nonnegative costs. The primary cost is larger than the secondary cost for each arc. Given a source node and a destination node, it is required to connect these in a path P, to which all other nodes are linked in one or more tree-like structures. The cost of the resulting tree is found from the primary costs of the arcs used in P and the secondary costs of all other arcs. A dynamic programming formulation is presented which finds a suboptimal solution to the problem, and the paper indicates the reasons for this formulation falling under certain circumstances.