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Unformatted text preview: ll be given for a method that involves an enumeration over all possible paths (in the objective or constraints). Hint. For each node i, let Pi denote the maximum of k∈P pk over all paths P from the source node 1 to node i (so P max = Pn ). (b) Carry out your method on the problem instance given in interdict_alloc_data.m. The data file contains the data a, xmax , B , and the graph incidence matrix A ∈ Rn×m , where −1 if edge j leaves node i +1 if edge j enters node i Aij = 0 otherwise. 130 Give P max⋆ , the optimal value of P max , and compare it to the value of P max obtained with uniform allocation of resources, i.e., with x = (B/m)1. Hint. Given a vector z ∈ Rn , AT z is the vector of edge differences: (AT z )j = zk − zl if edge j goes from node l to node k . 131 The following figure shows the topology of the graph in question. (The data file contains A; this figure, which is not needed to solve the problem, is shown here so you can visualize the graph.) Node 1 Node 2 Node 4 Node 3 Node 6 Node 5 Node 7 Node 8 Node 9 Node 10 15.5 Network sizing. We c...
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