The schematic diagram of the telecommunication network of GTC in a particular region is shown in Figure 3.1. Each node in the network represents a major network hub, while each edge in the network represents a link between two such hubs. In the figure, there is a vector containing two numbers along each edge. The first entry of the vector indicates the cost of sending one GBps of data along that edge (in “100 units), while the second entry indicates the bandwidth available along that edge (in 100GBps units). GTC is considering a request to provide a bandwidth of 600GBps between the points A and H in the network and is wondering what the minimum cost of providing this bandwidth would be.
This problem is a typical example of a minimum cost flow problem. The solution to the problem consists of a collection of edges in the network, which can be combined to form paths, and the amount of flow along each of the edges. The sum of the costs of this collection of edges, each weighted by the amount of flow it carries, is the minimum cost that has to be incurred to route the required amount of flow.
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