Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms

This paper establishes max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, it shows that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by the min-cut. The result (which is essentially optimal) establishes an important analogue of the famous 1-commodity max-flow min-cut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms.