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on sets of vertices of the graph. Instead of obeying
Kirchhoff's law, it is a requirement that, for every vertex set, the excess flow (the function mapping the set to its difference between flow in and flow out) can be at most the value given by the submodular function.
58:, with given capacities that specify lower and upper limits on the amount of flow per edge, as well as costs per unit flow along each edge. The goal is to find a system of flow amounts that obey the capacities on each edge, obey
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that the total amount of flow into each vertex equals the total amount of flow out, and have minimum total cost. In submodular flow, as well, one is given a
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Grötschel, M.; Lovász, L.; Schrijver, A. (1981), "The ellipsoid method and its consequences in combinatorial optimization",
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156:(1993), "A framework for cost-scaling algorithms for submodular flow problems",
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is a general class of optimization problems that includes as special cases the
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193:, Association for Computing Machinery, pp. 107–116,
35:, and the problem of computing a minimum-weight
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47:and Rick Giles, and can be solved in
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43:. It was originally formulated by
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226:Combinatorial optimization
21:combinatorial optimization
29:minimum-cost flow problem
166:10.1109/SFCS.1993.366842
64:submodular set function
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33:matroid intersection
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