Algorithm question 1. What variation of the augmenting path algorithm(for network flow) was proposed to ensure...
Algorithm question
1. What variation of the augmenting path algorithm(for network flow) was proposed to ensure that it ran in polynomial time?
Homework Answers
The answer to the question asked :
Polynomial time variant using gain-scaling was proposed to ensure that the augmented path algorithm ran in polynomial time.
This question is for variation of the augmenting path algorithm but there are no other details asked of the algorithm, but if you want to understand how to work with an algorithm or have any difficulty with it then you can refer to pdf of Kevin Wayne from this link https://www.cs.princeton.edu/~wayne/papers/gain-scaling_talk.pdf
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Algorithm question
1. What variation of the augmenting path algorithm(for network
flow) was proposed to ensure...
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
b) Starting with the flow given below, use the augmenting algorithm to find a maximal flow,...
b) Starting with the flow given below, use the augmenting algorithm to find a maximal flow, and the corresponding minimal cut, in this network 13,5 D 5,5 14,0 A 10,5 12,0 11,5 C 10,5
b) Starting with the flow given below, use the augmenting algorithm to find a maximal flow, and the corresponding minimal cut, in this network 13,5 D 5,5 14,0 A 10,5 12,0 11,5 C 10,5
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,...
For the network in the figure, apply the max-min flow control algorithm to assign sessions for...
For the network in the figure, apply the max-min flow control
algorithm to assign sessions for the following network. Three
different flows each with offering Poisson arrivals streams are
sharing the links in this network. The link capacities (equivalent
with the transmission rates for each transmission line) are marked
in the figure. The service times for a transmission line are
assumed to be exponentially distributed.
The session flow 1 has the path A -> B -> C -> D; Flow...
Algortithms Please answer question 7 using algorithm 3.5 7, /Analyze the Print Shortest Path algorithm (Algorithm...
Algortithms
Please answer question 7 using algorithm 3.5
7, /Analyze the Print Shortest Path algorithm (Algorithm 3.5) and show that it has a linear-time complexity Algorithm 3.5 Print Shortest Path Problem: Print the intermediate vertices on a shortest path from one vertex to another vertex in a weighted graph. Inputs: the array P produced by Algorithm 3.4, and two indices, q and r, of vertices in the graph that is the input to Algorithm 3.4. highest index of an intermediate...
Consider the following network. a. (16 pt.) With the indicated link costs, use Dijkstra’s shortest-path algorithm...
Consider the following network.
a. (16 pt.)
With the indicated link costs, use Dijkstra’s shortest-path
algorithm to compute the shortest path from “w” to
all network nodes. Show how the algorithm works by computing the
table below. Note: If there exists any tie in each step, choose the
left-most column first.
Step
N’
D(s),
p(s)
D(t),
p(t)
D(u),
p(u)
D(v),
p(v)
D(x),
p(x)
D(y),
p(y)
D(z),
p(z)
0
1
2
3
4
5
6
7
b. (7 pt.)
Construct the...
Problem 2. Apply Dijkstra's least-cost or shorted-path algorithm to the network shown on the right. Complete...
Problem 2. Apply Dijkstra's least-cost or shorted-path algorithm to the network shown on the right. Complete the table by filling the T, Lin), and Path on each row to show the result of each iteration. Result of the last iteration, 6, is already provided in red as a way to help you to verify if your iterations are performed correctly. (1 point each box, 30 points in total) Iteration I L(2) Path L(3) Path L(4) Path L(5) Path LO Path...
4. Given a network of 8 nodes and the distance between each node as shown in Figure 1: 4 1 7 0 4 4 6 6 Figure 1: Network graph of 8 nodes a) Find the shortest path tree of node 1 to all the other nod...
4. Given a network of 8 nodes and the distance between each node as shown in Figure 1: 4 1 7 0 4 4 6 6 Figure 1: Network graph of 8 nodes a) Find the shortest path tree of node 1 to all the other nodes (node 0, 2, 3, 4, 5, 6 and 7) using Dijkstra's algorithm. b) Design the Matlab code to implement Dijkstra's algorithm
4. Given a network of 8 nodes and the distance between each...
1. Say that we are given a maximum flow in the network. Then the capacity of one of the edges e i...
1. Say that we are given a maximum flow in the network. Then the capacity of one of the edges e is increased by 1. Give an algorithm that checks if the maximum flow has increased 2. When we increase the capacity of some edge by 5 can it be that the flow does not increase at all? 3. When we increase the capacity of an edge by 5, can the flow grow by 7? Please write time complexity for...
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...
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
b) Starting with the flow given below, use the augmenting algorithm to find a maximal flow, and the corresponding minimal cut, in this network 13,5 D 5,5 14,0 A 10,5 12,0 11,5 C 10,5
b) Starting with the flow given below, use the augmenting algorithm to find a maximal flow, and the corresponding minimal cut, in this network 13,5 D 5,5 14,0 A 10,5 12,0 11,5 C 10,5
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,...
For the network in the figure, apply the max-min flow control
algorithm to assign sessions for the following network. Three
different flows each with offering Poisson arrivals streams are
sharing the links in this network. The link capacities (equivalent
with the transmission rates for each transmission line) are marked
in the figure. The service times for a transmission line are
assumed to be exponentially distributed.
The session flow 1 has the path A -> B -> C -> D; Flow...
Algortithms
Please answer question 7 using algorithm 3.5
7, /Analyze the Print Shortest Path algorithm (Algorithm 3.5) and show that it has a linear-time complexity Algorithm 3.5 Print Shortest Path Problem: Print the intermediate vertices on a shortest path from one vertex to another vertex in a weighted graph. Inputs: the array P produced by Algorithm 3.4, and two indices, q and r, of vertices in the graph that is the input to Algorithm 3.4. highest index of an intermediate...
Consider the following network.
a. (16 pt.)
With the indicated link costs, use Dijkstra’s shortest-path
algorithm to compute the shortest path from “w” to
all network nodes. Show how the algorithm works by computing the
table below. Note: If there exists any tie in each step, choose the
left-most column first.
Step
N’
D(s),
p(s)
D(t),
p(t)
D(u),
p(u)
D(v),
p(v)
D(x),
p(x)
D(y),
p(y)
D(z),
p(z)
0
1
2
3
4
5
6
7
b. (7 pt.)
Construct the...
Problem 2. Apply Dijkstra's least-cost or shorted-path algorithm to the network shown on the right. Complete the table by filling the T, Lin), and Path on each row to show the result of each iteration. Result of the last iteration, 6, is already provided in red as a way to help you to verify if your iterations are performed correctly. (1 point each box, 30 points in total) Iteration I L(2) Path L(3) Path L(4) Path L(5) Path LO Path...
4. Given a network of 8 nodes and the distance between each node as shown in Figure 1: 4 1 7 0 4 4 6 6 Figure 1: Network graph of 8 nodes a) Find the shortest path tree of node 1 to all the other nodes (node 0, 2, 3, 4, 5, 6 and 7) using Dijkstra's algorithm. b) Design the Matlab code to implement Dijkstra's algorithm
4. Given a network of 8 nodes and the distance between each...
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...
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