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You have successfully computed a maximum s-t flow f for
a network G = (V; E) with integer edge capacities. Your
boss now gives you another network G that is identical to
G except that the capacity of exactly one edge is
decreased by one. You are also explicitly given the edge
whose capacity was changed. Describe how you can
compute a maximum flow for G in O( V + E ) time.
so
Case
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O m i Find a path from store on
edges that
carry
some flan in G
Olm 2 Find apath from u tot
on edges that carry some floesOlm 3 subtract a unit offlow on thiscombinedpath from SII f
gLm 4 Construct a residual graph forthe new flow f
Ohm 5 Run DFS DFS fron s to
find a path to it on Gf6 if no such path existsf is our new Max f too
otherwise
0 m use this path for one more
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