6.4. the Approximation Factor

We are now ready to finish the analysis of the approximation factor of the algorithm. Our goal is to bound the weight of the chosen feedback set, namely, w(F). To meet this end, we consider separately the chosen intra-saturated vertices and the chosen inter-saturated vertices. Recall, that in the ith iteration we add to F a subset F i = A i B i. The vertices in A i are intra-saturated by the flow of commodity f i , and hence, w(A i) d i. Using Theorem 6.2 we bound w(k i=1 B i) by w(I k). We apply Theorem 4.1 to the graph