Consider the directed graph shown below:
a) What is the minimum capacity cut through this graph (which is
the maximum flow in the network represented
by the graph) and which edges are
involved?
b) Using the ShortestAugmentingPath algorithm, find the flows
through each edge (the xij 's) that produce the
maximum flow.
Homework Answers
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Consider the directed graph shown below:
a) What is the minimum capacity cut through this graph...
4) Consider the network flow graph below, where each arc is labeled with the maximum capacity...
4) Consider the network flow graph below, where each arc is labeled with the maximum capacity of that link in the flow network. A 25C 15 - 10,- -* YD 15 35 20 40 10 X 2 (a) Use the Ford-Fulkerson Algorithm to determine the maximum total flow from source to sink in this network. Start with the path s B DA Ct and list (in order) the remaining paths added and the total flow after each path is added....
Algorithms Below is a directed graph with edge capacities. Find the maximum flow from A to K. Write down the augmenting paths you chose, the residual capacities, and the graph with that maximum fHow....
Algorithms
Below is a directed graph with edge capacities. Find the maximum flow from A to K. Write down the augmenting paths you chose, the residual capacities, and the graph with that maximum fHow. Also give the minimum cut which shows that the flow is maximum.
Below is a directed graph with edge capacities. Find the maximum flow from A to K. Write down the augmenting paths you chose, the residual capacities, and the graph with that maximum fHow. Also...
Question 2 for a network with source at vertex A and target at vertex H The matrix at right shows the capacities o 5 0...
Question 2 for a network with source at vertex A and target at vertex H The matrix at right shows the capacities o 5 0 06 10 0 00 6 0 0 4 (a) Find a minimum cut. Specify the partition of the vertices, 0 0080 0 0 000 0 0 0 000 0 0700 0 0020 0000 0 0 0 0 the edges making up the cut, and the value of the cut 09 7 0 0 8 0...
5 Network Flow, 90p. Consider the below flow network, with s the source and t the sink. 5 4 1. (10p) Draw a flow with value 8. (You may write it on top of the edges in the graph above, or draw a...
5 Network Flow, 90p. Consider the below flow network, with s the source and t the sink. 5 4 1. (10p) Draw a flow with value 8. (You may write it on top of the edges in the graph above, or draw a new graph.) You are not required to show how you construct the flow (though it may help you to apply say the Edmonds-Karp algorithm). 2. (5p) List a cut with capacity 8. (You may draw it in...
graph below represents a network and the capacities are the sumber written on edges. The source is node a, and the target is node h. a. 10 (e) Show a fow of size 7 units going from the source a t...
graph below represents a network and the capacities are the sumber written on edges. The source is node a, and the target is node h. a. 10 (e) Show a fow of size 7 units going from the source a to the target h. (Write on the graph, next to the capacity, how many units of flow go through each edge.) (b) Consider the cut (L, R), wbere L (o) and R-(d.e.cf.s.Al, Indicate the edges crosig show that this cut...
Consider the following weighted undirected graph.
Consider the following weighted undirected graph. (a) Explain why edge (B, D) is safe. In other words, give a cut where the edge is the cheapest edge crossing the cut. (b) We would like to run the Kruskal's algorithm on this graph. List the edges appearing in the Minimum Spanning Tree (MST) in the order they are added to the MST. For simplicity, you can refer to each edge as its weight. (c) 1We would like to run the Prim's algorithm on this...
4. (30 Points) Consider the following network, where the numbers associated with the edges are the...
4. (30 Points) Consider the following network, where the numbers associated with the edges are the edge capacities: 9 7 6 3 a. Show the final graph G, flow graph Gf, and residual graph Gr after the simple maximum-flow algorithm (using the correct version) terminates b. What is the maximum flow of the network?
Consider the following weighted, directed graph G. There are 7 vertices and 10 edges. The edge list E is as follows:
Consider the following weighted, directed graph G. There are 7 vertices and 10 edges. The edge list E is as follows:The Bellman-Ford algorithm makes |V|-1 = 7-1 = 6 passes through the edge list E. Each pass relaxes the edges in the order they appear in the edge list. As with Dijkstra's algorithm, we record the current best known cost D[V] to reach each vertex V from the start vertex S. Initially D[A]=0 and D[V]=+oo for all the other vertices...
1. Consider a directed graph with distinct and non-negative edge lengths and a source vertex s....
1. Consider a directed graph with distinct and non-negative edge lengths and a source vertex s. Fix a destination vertex t, and assume that the graph contains at least one s-t path. Which of the following statements are true? [Check all that apply.] ( )The shortest (i.e., minimum-length) s-t path might have as many as n−1 edges, where n is the number of vertices. ( )There is a shortest s-t path with no repeated vertices (i.e., a "simple" or "loopless"...
Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears...
Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears at most once) from s to t that goes via v. Create a flow network by making v a source. Add a new vertex Z as a sink. Join s, t with two directed edges of capacity...
4) Consider the network flow graph below, where each arc is labeled with the maximum capacity of that link in the flow network. A 25C 15 - 10,- -* YD 15 35 20 40 10 X 2 (a) Use the Ford-Fulkerson Algorithm to determine the maximum total flow from source to sink in this network. Start with the path s B DA Ct and list (in order) the remaining paths added and the total flow after each path is added....
Algorithms
Below is a directed graph with edge capacities. Find the maximum flow from A to K. Write down the augmenting paths you chose, the residual capacities, and the graph with that maximum fHow. Also give the minimum cut which shows that the flow is maximum.
Below is a directed graph with edge capacities. Find the maximum flow from A to K. Write down the augmenting paths you chose, the residual capacities, and the graph with that maximum fHow. Also...
Question 2 for a network with source at vertex A and target at vertex H The matrix at right shows the capacities o 5 0 06 10 0 00 6 0 0 4 (a) Find a minimum cut. Specify the partition of the vertices, 0 0080 0 0 000 0 0 0 000 0 0700 0 0020 0000 0 0 0 0 the edges making up the cut, and the value of the cut 09 7 0 0 8 0...
5 Network Flow, 90p. Consider the below flow network, with s the source and t the sink. 5 4 1. (10p) Draw a flow with value 8. (You may write it on top of the edges in the graph above, or draw a new graph.) You are not required to show how you construct the flow (though it may help you to apply say the Edmonds-Karp algorithm). 2. (5p) List a cut with capacity 8. (You may draw it in...
graph below represents a network and the capacities are the sumber written on edges. The source is node a, and the target is node h. a. 10 (e) Show a fow of size 7 units going from the source a to the target h. (Write on the graph, next to the capacity, how many units of flow go through each edge.) (b) Consider the cut (L, R), wbere L (o) and R-(d.e.cf.s.Al, Indicate the edges crosig show that this cut...
4. (30 Points) Consider the following network, where the numbers associated with the edges are the edge capacities: 9 7 6 3 a. Show the final graph G, flow graph Gf, and residual graph Gr after the simple maximum-flow algorithm (using the correct version) terminates b. What is the maximum flow of the network?
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