Approximate Max--ow Min-(multi)cut Theorems and Their Applications

Consider the multicommodity ow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate max-ow min-multicut theorem: min multicut O(log k) max ow min multicut; where k is the number of commodities. Our proof is constructive; it enables us to nd a multicut within O(log k) of the max ow (and hence also the optimal multicut). In addition, the proof technique provides a uniied framework in which one can also analyse the case of ows with speciied demands, of Leighton-Rao and Klein et.al., and thereby obtain an improved bound for the latter problem.