Consider an s-t flow network G = (V;E). Assume that every edge e has an integer

Question

Consider an s-t flow network G = (V;E). Assume that every edge e has an
integer capacity c(e) > 0. There may be several s-t minimum (capacity) cuts in G. Let us
say that an s-t minimum (capacity) cut (S; T) is thin if the number of edges that (S; T) cuts
is less than or equal to the number of edges that every other minimum cut (S0; T0) cuts.
Design an algorithm that nds a thin minimum cut (S; T). Prove its correctness.
Answer. Given source node s and sink node t, we can compute maximum
flow and capacity of minimum cut in network G = (V;E) using Ford-Fulkerson Algorithm.

Explanation / Answer

Answer

observation as an s-t overflow network G= (V, E).

presume that every edge e has an figure capacity c (e)>0.

Given font node s and sink node t, we can add maximum flow and competence of minimum cut in network G= (V, E) by a ford-Fulkerson algorithm.

Algorithm:

consider as each of the limits of the residual graph, in which the initial place and the sink edge fit in to V.

If from as

Spring, s is available and from the sink, the t is accessible then, there is a blockage edge.

The algorithm is person proved by the reachability.

If s and t are not reachable by the font and the sink respectively, then augment the flow on the path beginning s to t will not be achievable.

And then by increasing the flair on the edge (source and the sink) will not growth the maximum flow.

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