A New Min-Cut Max-Flow Ratio for Multicommodity Flows
We present an improved bound on the min-cut max-flow ratio for multicommodity flow problems with specified demands. To obtain the numerator of this ratio, capacity of a cut is scaled by the demand that has to cross the cut. In the denominator, the maximum concurrent flow value is used. Our new bound is proportional to log(k*) where k* is the cardinality of the minimal vertex cover of the demand graph.
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