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4. (30 Points) Consider the following network, where the numbers associated with the edges are the...
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,...
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....
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...
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, 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...
11) c) Consider the following network diagram of a supply system, where the numbers associated with...
11) c) Consider the following network diagram of a supply system, where the numbers associated with the arrows represent unit shipping costs (from factories to warehouses). Our goal is to minimize the total shipping cost. Using Vogel's approximation method, find a Basic Feasible Solution to the problem and find the corresponding shipping cost. DEMAND FACTERIES WARENOUSES CAPAEITY 20 5 1-4 15 20 2 13 20 10 3
11) c) Consider the following network diagram of a supply system, where the...
solve with steps 1. (20 points) True or false. Justify. Every planar graph is 4-colorable /2 The number of edges in a simple graph G is bounded by n(n 1) where n is the number of vertices. The number...
solve with steps
1. (20 points) True or false. Justify. Every planar graph is 4-colorable /2 The number of edges in a simple graph G is bounded by n(n 1) where n is the number of vertices. The number of edges of a simple connected graph G is at least n-1 where n is the number of vertices. Two graphs are isomorphic if they have the same number of vertices and 1) the same mumber of edges
1. (20 points)...
4. (30 points) Consider the following 2 x 2 system Axb (a) (10 points) Use the...
4. (30 points) Consider the following 2 x 2 system Axb (a) (10 points) Use the elimination algorithm discussed in class and on the homework to turn Ax the form Ux = c, where U is an upper triangular matrix and c is a modified version of b. binto (b) (10 points) Continue the elimination algorithm to turn Ux-c from part (a) into the form Dx d. where D is a diagonal matrix and d is a modified version of...
Other answer is incorrect Problem 1. (15 points) Consider an undirected connected graph G = (V,...
Other answer is incorrect
Problem 1. (15 points) Consider an undirected connected graph G = (V, E) with edge costs ce > 0 for e € E which are all distinct. (a) [8 points). Let E' CE be defined as the following set of edges: for each node v, E' contains the cheapest of all edges incident on v, i.e., the cheapest edge that has v as one of its endpoints. Is the graph (V, E') connected? Is it acyclic?...
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,...
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....
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...
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...
11) c) Consider the following network diagram of a supply system, where the numbers associated with the arrows represent unit shipping costs (from factories to warehouses). Our goal is to minimize the total shipping cost. Using Vogel's approximation method, find a Basic Feasible Solution to the problem and find the corresponding shipping cost. DEMAND FACTERIES WARENOUSES CAPAEITY 20 5 1-4 15 20 2 13 20 10 3
11) c) Consider the following network diagram of a supply system, where the...
solve with steps
1. (20 points) True or false. Justify. Every planar graph is 4-colorable /2 The number of edges in a simple graph G is bounded by n(n 1) where n is the number of vertices. The number of edges of a simple connected graph G is at least n-1 where n is the number of vertices. Two graphs are isomorphic if they have the same number of vertices and 1) the same mumber of edges
1. (20 points)...
4. (30 points) Consider the following 2 x 2 system Axb (a) (10 points) Use the elimination algorithm discussed in class and on the homework to turn Ax the form Ux = c, where U is an upper triangular matrix and c is a modified version of b. binto (b) (10 points) Continue the elimination algorithm to turn Ux-c from part (a) into the form Dx d. where D is a diagonal matrix and d is a modified version of...
Other answer is incorrect
Problem 1. (15 points) Consider an undirected connected graph G = (V, E) with edge costs ce > 0 for e € E which are all distinct. (a) [8 points). Let E' CE be defined as the following set of edges: for each node v, E' contains the cheapest of all edges incident on v, i.e., the cheapest edge that has v as one of its endpoints. Is the graph (V, E') connected? Is it acyclic?...
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