Question: 1 . ( Flow fundamental ) Suppose you are given a directed graph G = ( V , E ) with a positive integer capacity

1 . (

Flow fundamental

)

Suppose you are given a directed graph G

= (

,

)

with a positive integer capacity ce on each edge e

,

a designated source s in V

,

and a designated sink t in V

.

You are also given an integer maximum s

t flow in G

,

defined by a flow value fe on each edge e

.

Now suppose we pick a specific edge e in E and decrease its capacity by one unit. Show how to find a maximum flow in the resulting capacitated graph in time O

(

+

),

where m is the number of edges in G and n is the number of vertices in G

.

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