Approximate Max-Flow Min-Cut Theorems (Course Notes Extension for COMP5703)

In this report, we discuss two approximate max-flow min-cut theorems that first introduced by Tom Leighton and Satish Rao in 1988 [9] and extended in 1999 [10] for uniform multicommodity flow problems. In the theorems they first showed that for any n-node multicommodity flow problem with uniform demands, the max-flow is a Ω(log n) factor smaller than the min-cut; further,they proved the max-flow is always within a θ(log n)factor of the cut. These two theorems also have substantial applications to the field of approximation algorithms, we briefly discuss two basic examples in chapter 3. Most of the content of this report are referencing [10] [9] [12] [13] [15] [1] [2] and [6].