Applying flow analysis methods to the problem of network design

One of the reasons that the communication network design problem is so difficult is that there are numerous competing objectives. The following criteria must be met in an optimum design: minimize the cost of the resulting network; maximize flow between all pairs of nodes; allow multiple commodities to simultaneously use the network; synthesize an optimum topology for the network; and provide an efficient routing protocol for messages. The approach taken in this paper is to relax one of the goals by assuming that only one source-sink pair at a time uses the network. The single commodity approach produces a minimum weight topology which can be mapped to multiple commodities by assigning link capacities proportionate to the edge weights. Finally, some post-processing may be necessary to account for more complex cost functions, such as the one above, where both capacity and distance affect cost.