Question 4 (20 marks) Let N be the network below, where ax and y are the...
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 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...
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...
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?
4. Use Ford-Fulkerson algorithm to find the maximum flow from source node 0 to the sink node 5 in 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 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...
1. Linear programming can be used to calculate the maximum flow in a network from the source s, to the sink t. Which of the following statements below gives the correct objective function, and number of constraints for applying a linear program for computing maximum flow in the following graph? In this graph, the maximum capacity of each edge is given as the number next to the corresponding edge. The flow along an edge eſi, j) is denoted by fij....