Problem 2. Find the maximum flow in the flow network shown in figure 1. In the flow network 's' is the source vertex and t' is the destination vertex. The capacity of each of the edges are given in the figure. v1 v2 4 t 10 v3 9 v4 6.
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Problem 2.
Find the maximum flow in the flow network shown in figure 1. In the flow network ‘s’ is the source vertex and ‘t’ is the destination vertex. The capacity of each of the edges are given in the figure.
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- Define an augmenting path in a flow network. Apply Ford Fulkerson's method to compute the maximum flow in a given network. S 3 3 2 A 1 B 1 2 1c.) Figure 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 Figure 2 (draw a picture like Figure 2, and specify the amount of flow in the box for each edge), and also say what its capacity is.2. Find the maximum flow from source (node 1) to destination (node 6) from the following flow graph. Show the residual network at each step. 2 10 8. 1 10 3 5 12
- Given the following flow graph. Determine the maximum flow from S to T. Be sure to show all the iterations including the residual graphs. 10 8 10 10 10 4 9Compute 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.Using Ford-Fulkerson algorithm, determine the maximum flow from the source S to sink t in the graph provided.
- Find the maximum flow from JCT A to JCT G for the graph in filek as done 1. Apply Floyd-Warshall algorithm on the following graph. Show all your work. nments to Sumon Ahmed 3 3 7 4 4 2. Find the maximum flow from source (node 1) to destination (node 6) from the following flow graph. Show the residual network at each step. 10:19 AM 67°F Haze A O 4) 1/3/20220/16 0/12 0/8 0/4 22 0/8 0/5 0/11 VA 0/13 0/14 V5 0/2 0/11 0/10 Each edge is annotated with the current flow (initially zero) and the edge's capacity. In general, a flow of x along an edge with capacity y is shown as x/y. (a) Show the residual graph that will be created from this network with the given (empty) flow. In drawing a residual graph, to show a forward edge with capacity x and a backward edge with capacity y, annotate the original edge *; y. (b) What is the bottleneck edge of the path (S, V₁, V3, V5, t) in the residual graph you have given in answer to part (a) ? (c) Show the network with the flow (s, V₁, V3, V5, t) that results from augmenting the flow based on the path of the residual graph you have given in answer to part (a). (d) Show the residual graph for the network flow given in answer to part (c). (e) What is the bottleneck edge of the path (s, v3, v4, t) in the residual graph you have given in answer to part (d) ?
- a) Show the residual graph for the network flow given in answer to part b) What is the bottleneck edge of the path (?, ?3, ?4, ?) in the residual graph you have given in answer to part (a) Show the network with the flow that results from augmenting the flow based on the path (?, ?3, ?4, ?) of the residual graph you have given in answer to part (a)Given the flow network below, 1) Draw the residual graph for the flow shown in the figure 2) Add an augmenting path to achieve the final maxflow. 3) Draw the final residual graph reflecting the augment path from 2) You need to submit the residual graphs from 1) and 3) only.(a) Draw an undirected graph G1 represented by the following adjacency matrix: 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 Does G1 contain a Hamiltonian cycle? Explain (b) Determine which pairs of graphs G1 in part (a) and G2 and G3 shown below are isomorphic and which are not, and explain your answer. If you use any invariant property in your argument, explain why this property is an invariant. Tex our answer. t 2 G2 G3 5. 7 8.