The topic is network flow Kleinberg, Jon. Algorithm Design $($p$.419,$ q$.10)$ Suppose you are given a directed graph G$=($V$,$ E$).$ This graph has a positive integer capacity c$\_$e on each edge, a source s in V$,$ a sink t in V$.$ You are also given a maximum s$-$t flow through G : f$.$ You know that this flow is acyclic $($no cycles with positive flow all the way around the cycle$),$ and every flow f$\_$e in f has an integer value. Now suppose we pick an edge e$^*$ and reduce its capacity by $1$ unit. Show how to find a maximum flow in the resulting graph G$^*$ in time O$($m$+$n$),$ where n$=|$V$|$ and m$=|$E$|.$