An Approximate Max-Flow Min-Cut Relation for Unidirected Multicommodity Flow, with Applications

@article{Klein1995AnAM,
  title={An Approximate Max-Flow Min-Cut Relation for Unidirected Multicommodity Flow, with Applications},
  author={Philip N. Klein and Satish Rao and Ajit Agrawal and R. Ravi},
  journal={Combinatorica},
  year={1995},
  volume={15},
  pages={187-202}
}
In this paper , we prove the first approximate max-flow min-cut theorem for undirected mul t i commodi ty flow. We show tha t for a feasible flow to exist in a mul t icommodi ty problem, it is sufficient t ha t every cut ' s capacity exceeds its demand by a factor of O(logClogD), where C is the sum of all finite capacities and D is the sum of demands . Moreover, our theorem yields an a lgor i thm for finding a cut tha t is approximately min imum relative to the flow tha t must cross it. We use… CONTINUE READING
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