Integer Programming Approaches to the Problem of Network Upgrading

The problem of reducing the diameter of a network by upgrading some nodes (i.e., replacing the routers at such nodes by newer models) is considered. The minimization of the total cost to make the diameter no more than U (a given constant) is known to be NP-hard. We discuss integer programming approaches to this problem; some of them aim to obtain exact solutions, and the last is heuristic. Computational results reveal tremendous differences in various formulations for exact solutions, and a clear computational advantage of the heuristic algorithm.