4. Use Ford-Fulkerson algorithm to find the maximum flow from source node 0 to the sink node 5 in the following network.
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4. Use Ford-Fulkerson algorithm to find the maximum flow from source node 0 to the sink node 5 in...
QUESTION Use the Augmenting Paths method to find the maximum flow from the source node s...
QUESTION Use the Augmenting Paths method to find the maximum flow from the source node s to sink node tin the flow network represented by the graph below. In your solution show the algorithm iterations, and for each iteration show the augmenting path and that path's flow. Attach File Browse My Computer
6. Show the trace of execution of the algorithm of Ford and Fulkerson on the following...
6. Show the trace of execution of the algorithm of Ford and Fulkerson on the following graph, using A and Z as source and sink. Show the minimum cut on this graph, and compute its capacity. 21 3 В E H 5 20 2 12 1.5 8 A N D G 23 24 1.2 2 18 1.4 13 с F 1.5 3
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....
We will look at how the Ford-Fulkerson Algorithm operates on the following network.
We will look at how the Ford-Fulkerson Algorithm operates on the following network.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,...
Find the shortest path algorithm tables (for the graph on the homework sheet) using the (a)...
Find the shortest path algorithm tables (for the graph on the
homework sheet) using the
(a) Dijkstra algorithm
(b) Ford-Fulkerson algorithm
Label the columns B,C,D from left to right. Node A is the root
node.
Use pointers for only the Ford Fulkerson algorithm as in the
Networks and Grids book.
(c) Let the link number be bandwidth (data rate). Create the
routing table that allows you find paths to the root node that
maximize the bottleneck bandwidth
Uhe
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...
(b) A source in a directed graph is a node with no incoming edges. A sink...
(b) A source in a directed graph is a node with no incoming edges. A sink is a node with no outgoing edges. Assume that we know that every DAG has at least one sink. Use this fact to explain why every DAG must have at least one source. (c) Consider the following graph algorithm which takes a DAG G as input. function COMPUTESOMETHING(DAG G) Lempty linked list S stack of all source nodes in G while S is non-empty...
Question 4 (20 marks) Let N be the network below, where ax and y are the...
Question 4 (20 marks) Let N be the network below, where ax and y are the source and sink respectively, and the arc S capacities are shown next to each arc. An initial flow of this network is given in parentheses 3(0) 6(0) 5(0) 4(0) 3(1) 2(0) X 2(1) 2(0) 3(1), 5(1) 4(0) 2(2) 2.5(1) V Starting from the given flow, use the labelling algorithm to find a maximum flow in N. Show every stage of the algorithm. State the...
You are given a flow network G with n >4 vertices. Besides the source sand the sink t, you are...
You are given a flow network G with n >4 vertices. Besides the source sand the sink t, you are also given two other special vertices u and v belonging to G. Describe an algorithm which finds a cut of the smallest possible capacity among all cuts in which vertex u is at the same side of the cut as the sources and vertex v is at the same side as sink t. Hint: it is enough to ad two...
Consider the network shown below. Use Dijkstra's algorithm to find the shortest paths from node a...
Consider the network shown below. Use Dijkstra's algorithm to find the shortest paths from node a to all other nodes. Enter your answers in the a shortest path answers in the following format: node-node-node. For example, if the ssignment link. Enter the shortest path from a to c is through node b, you would enter the answer as: a-b-c 3 5 6 6
QUESTION Use the Augmenting Paths method to find the maximum flow from the source node s to sink node tin the flow network represented by the graph below. In your solution show the algorithm iterations, and for each iteration show the augmenting path and that path's flow. Attach File Browse My Computer
6. Show the trace of execution of the algorithm of Ford and Fulkerson on the following graph, using A and Z as source and sink. Show the minimum cut on this graph, and compute its capacity. 21 3 В E H 5 20 2 12 1.5 8 A N D G 23 24 1.2 2 18 1.4 13 с F 1.5 3
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....
We will look at how the Ford-Fulkerson Algorithm operates on the following network.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,...
Find the shortest path algorithm tables (for the graph on the
homework sheet) using the
(a) Dijkstra algorithm
(b) Ford-Fulkerson algorithm
Label the columns B,C,D from left to right. Node A is the root
node.
Use pointers for only the Ford Fulkerson algorithm as in the
Networks and Grids book.
(c) Let the link number be bandwidth (data rate). Create the
routing table that allows you find paths to the root node that
maximize the bottleneck bandwidth
Uhe
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...
(b) A source in a directed graph is a node with no incoming edges. A sink is a node with no outgoing edges. Assume that we know that every DAG has at least one sink. Use this fact to explain why every DAG must have at least one source. (c) Consider the following graph algorithm which takes a DAG G as input. function COMPUTESOMETHING(DAG G) Lempty linked list S stack of all source nodes in G while S is non-empty...
Question 4 (20 marks) Let N be the network below, where ax and y are the source and sink respectively, and the arc S capacities are shown next to each arc. An initial flow of this network is given in parentheses 3(0) 6(0) 5(0) 4(0) 3(1) 2(0) X 2(1) 2(0) 3(1), 5(1) 4(0) 2(2) 2.5(1) V Starting from the given flow, use the labelling algorithm to find a maximum flow in N. Show every stage of the algorithm. State the...
Consider the network shown below. Use Dijkstra's algorithm to find the shortest paths from node a to all other nodes. Enter your answers in the a shortest path answers in the following format: node-node-node. For example, if the ssignment link. Enter the shortest path from a to c is through node b, you would enter the answer as: a-b-c 3 5 6 6
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