# Scaling Methods for Finding a Maximum Free Multiflow of Minimum Cost

@article{Goldberg1997ScalingMF, title={Scaling Methods for Finding a Maximum Free Multiflow of Minimum Cost}, author={Andrew V. Goldberg and Alexander V. Karzanov}, journal={Math. Oper. Res.}, year={1997}, volume={22}, pages={90-109} }

Suppose we are given an undirected graph with nonnegative integer-valued edge capacities and costs in which a subset of nodes is specified. We consider the problem of finding a collection of flows between arbitrary pairs of specified nodes such that the capacity constraints are satisfied and the sum of costs of flows is minimum, provided that the sum of values of flows is maximum. It is known that this problem has a half-integer optimal solution and such a solution can be found in strongly… CONTINUE READING

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## A Cost-Scaling Algorithm for Minimum-Cost Node-Capacitated Multiflow Problem

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## Min-cost multiflows in node-capacitated undirected networks

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## On Min-Cost Multiflow Problem in Node-Capacitated Undirected Networks

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