Is max flow the same as min cut?
4. Max-Flow Min-Cut Theorem. The max-flow min-cut theorem states that the maximum flow through any network from a given source to a given sink is exactly equal to the minimum sum of a cut.
Why is min cut equal to max flow?
The Max-Flow/Min-Cut Theorem says that there exists a cut whose capacity is minimized (i.e. c(S, T) = val(f)) but this only happens when f itself is the maximum flow of the network! Therefore, in any flow network (G, s, t, c), the value of the maximum flow equals the capacity of the minimum cut in the network.
How do you prove maximum flow?
Lemma: For any flow f and any s-t cut (S, T), we have |f| ≤ ||S, T||. (This proves that the value of the max flow is less than or equal to the size of the min cut.) This is the method we will use to find a flow whose value equals the value of a cut (i.e. the max flow).
How is min cut calculated?
1) Run Ford-Fulkerson algorithm and consider the final residual graph. 2) Find the set of vertices that are reachable from the source in the residual graph. 3) All edges which are from a reachable vertex to non-reachable vertex are minimum cut edges.
What is the maximum flow value?
The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem.
What is a cut S T )? *?
In a flow network, an s–t cut is a cut that requires the source and the sink to be in different subsets, and its cut-set only consists of edges going from the source’s side to the sink’s side. The capacity of an s–t cut is defined as the sum of the capacity of each edge in the cut-set.
Is Min cut unique?
a. The mincut might not be unique. Consider a network flow that is two edges (s,u) and (u, t) both having the same capacity. There is only one max flow, but there are two min cuts.