Closure problem

By the max-flow min-cut theorem, a minimum cut, and the optimal closure derived from it, can be found by solving a maximum flow problem.

[1] Alternative algorithms for the maximum closure problem that do not compute flows have also been studied.

Each target needs a certain amount of resources to be allocated to it in order to perform a successful attack.

The optimal set of targets to attack, to obtain the most value for the resources expended, can be modeled as a closure problem.

[1][8] The problem of planning a freight delivery system may be modeled by a network in which the vertices represent cities and the (undirected) edges represent potential freight delivery routes between pairs of cities.

Each route can achieve a certain profit, but can only be used if freight depots are constructed at both its ends, with a certain cost.

The problem of designing a network that maximizes the difference between the profits and the costs can be solved as a closure problem, by subdividing each undirected edge into two directed edges, both directed outwards from the subdivision point.