Approximate max-flow min-(multi)cut theorems and their applications

@inproceedings{Garg1993ApproximateMM,
  title={Approximate max-flow min-(multi)cut theorems and their applications},
  author={Naveen Garg and Vijay V. Vazirani and Mihalis Yannakakis},
  booktitle={STOC},
  year={1993}
}
Consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate max-flow min-multicut theorem: min multicut < max flow < min multicut, O(log k) where k is the number of commodities. Our proof is constructive; it enables us to find a multicut within O(logk) of the max flow (and hence also the optimal multicut). In addition, the proof technique provides a unified framework in which one can also analyse the case of flows… CONTINUE READING

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