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Optimal network design
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<p>Optimal network design is a problem in <a href="/facts/Combinatorial_optimization/PTcloS79">combinatorial optimization</a>. It is an abstract representation of the problem faced by states and municipalities when they plan their road network. Given a set of locations to connect by roads, the objective is to have a short traveling distance between every two points. More specifically, the goal is to minimize the <i>sum</i> of shortest distances, where the sum is taken over all pairs of points. For each two locations, there is a number representing the cost of building a direct road between them. A decision must be made about which roads to build with a fixed budget. </p>