e 2 shows a flow network on which an s-t flow has been computed. The capacity of each edge appears as a label next to the edge, and the numbers in boxes give the amount of flow sent on each edge. (Edges without boxed numbers have no flow being sent on them.) What is the value of the flow in Figure 2? Is this a maximum (s,t) flow in this graph? d). Find a maximum flow from s to t in Figur

Apply the Network flow maximization algorithm in the text book  to the network below one step at a time. At each step, show diagrams of the flow graph Gf and the residual graph Gr to each diagram to describe how you obtained it from the previous diagram. In particular, describe the policy used to select an augmenting path from s to t for adding to the flow graph when multiple options were available. What is the termination condition for your algorithm? Prove that your solution is correct

g) Show the residual graph for the network flow given in answer to part (c). What is the bottleneck edge of the path (?, ?2, ?3, ?1, ?4, ?) in the residual graph you have given in answer to part (g) ? Show the network with the flow that results from augmenting the flow based on the path (?, ?2, ?3, ?1, ?4, ?) of the residual graph you have given in answer to part (g).

Consider the flow network shown in the following figure (left), where the label next to each arc is its capacity, and the initial s-t flow on right.  (b) Apply the Ford-Fulkerson algorithm to N starting from the flow f. The augmenting path used in each step of the algorithm must be given.  (c) Give the cut that corresponds to the maximum flow obtained in (b), which is suggested in the Max-Flow-Min-Cut theorom.

a. Find the general flow pattern of the network shown in the figure. b. Assuming that the flow must be in the directions indicated, find the minimum flows in the branches denoted by x2, x3, x4, and X5. 40 40 =HF Xyx D 30 40 80 60 <100 90

Compute the maximum flow in the following flow network using Ford-Fulkerson's algorithm. 12 8 14 15 11 2 5 1 3 d 7 f 6 What is the maximum flow value? A minimum cut has exactly which vertices on one side? 4.

4. (1) Draw a transition graph for the dfa M={Q,E,8,q,,F ), where Q={q,,91»92 }; E = {a,b},F = {qo,92} and ở is definded as S(90,a) = q,,8(q,b) =q,,5(q,,a)=q0,8(q,,b) =q2,8(q2,a) =q2,8(q2,b) =q2 (2) Give the language accepted by the above dfa.

How do I find the minimum capacity of an s-t cut in this flow network?

The input is a 20×20 matrix and the filter (aka kernel) is a 5×5 matrix. We set stride = 1 and no zero-padding. What is the shape of the output matrix

Algorithm: Network Flow(Maximu Flow, Ford-Fulkerson) and Application of Flow (Minimum Cuts, Bipartite Matching)   Consider a flow network and an arbitrary s, t-cut (S, T). We know that by definition s must always be on the S "side" of a cut and t is always going to be on the T "side" of the cut. Obviously, this is true for any cut. Now, consider minimum cuts. This is obviously still true for s and t, but what about other vertices in the flow network? Are there vertices that will always be on one side or the other in every minimum cut?   Let's define these notions more concretely. • We say a vertex v is source-docked if v ∈ S for all minimum cuts (S, T). • We say a vertex v is sink-docked if v ∈ T for all minimum cuts (S, T). • We say a vertex v is undocked if v is neither source-docked nor sink-docked. That is, there exist minimum cuts (S, T) and (S 0 , T0 ) such that v ∈ S and v ∈ T'   Give an algorithm that takes as input a flow network G and assigns each vertex to one of the three…