Algorithm Design

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Chapter 7 Network Flow
(7.19) The number of aug//1entations in a scaling phase is at most 2//1.
Proof. The statement is clearly true in the first scaling phase: we can use
each of the edges out of s only for at most one augmentation in that phase.
Now consider a later scaling phase A, and let fp be the flow at the end of the
previous scaling phase. In that phase, we used A’ = 2A as our parameter. By
(7.18), the maximum flow f* is at most v(f*)