4. (i)Show how the analysis of the flows in a network with several sources and sinks can be reduced to the standard case by the addition of a new 'source vertex' and 'sink vertex'. (ii) Illustrate your answer to part (i) with reference to the network in the following figure. v 3 A 3 1 W 6 B W 2 5 3 v C W 7 5

4. (i)Show how the analysis of the flows in a network with several sources and sinks can be reduced to the standard case by the addition of a new 'source vertex' and 'sink vertex'. (ii) Illustrate your answer to part (i) with reference to the network in the following figure. v 3 A 3 1 W 6 B W 2 5 3 v C W 7 5

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter8: Network Models

Section8.3: Maximum-flow Problems

Problem 11P

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0/16 0/12 0/8 0/4 22 0/8 0/5 0/11 VA 0/13 0/14 V5 0/2 0/11 0/10 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, annotate the original edge *; y. (b) What is the bottleneck edge of the path (S, V₁, V3, V5, t) in the residual graph you have given in answer to part (a) ? (c) Show the network with the flow (s, V₁, V3, V5, t) that results from augmenting the flow based on the path of the residual graph you have given in answer to part (a). (d) Show the residual graph for the network flow given in answer to part (c). (e) What is the bottleneck edge of the path (s, v3, v4, t) in the residual graph you have given in answer to part (d) ?
How can vector network analyser be used to find SS1 parameters?
Let’s consider the directed graph with unweighted links presented in Figure 4.12. Thisgraph is similar to the previous graph except by one missing link between A and E.Write networking code to describes how to create the new links dataset and then search for the existing cycles within the directed graph. ans in 20 min.or asap
Question 1 Refer to the following network flow and state the min cut, of the graph G. S 3/7 6/6 -5/5 (s,v1),(s,v3),(s,v2) 1/1 (v1,v4), (v1,v3),(s,v3),(s,v2) O (v4,t).(v3,t).(v5,t) O (s,v2),(v2,v3),(v2,v5) 0/3 -2/2- 4/5 -2/3 6/6 6/8
-With respect to the performance model, it should be implemented efficiently. Your answer Ring the network in a ring topology comes back around to the first node, creating a complete circuit. to a bus network, rings have nodes daisy chained, but the end of Your answer ----This part includes defining the problem, designing the corresponding model, and devising a set of experiments for the formulated simulation model.
Consider the flow network G shown in figure 1 with source s and sink t. The edge capacities are the numbers given near each edge. (a) Find a maximum flow in this network. Once you have done this, draw a copy of the original network G and clearly indicate the flow on each edge of G in your maximum flow. (b) Find a minimum s-t cut in the network, i.e. name the two (non-empty) sets of vertices that define a minimum cut. Also, say what its capacity is. g C 4 3 6 d b 3 Fig.1 A flow network, with sources and sink t. The numbers next to the edges are the capacities.
Consider the flow network G shown in figure 1 with source s and sink t. The edge capacities are the numbers given near each edge. (a) Find a maximum flow in this network. Once you have done this, draw a copy of the original network G and clearly indicate the flow on each edge of G in your maximum flow. (b) Find a minimum s-t cut in the network, i.e. name the two (non-empty) sets of vertices that define a minimum cut. Also, say what its capacity is. 3 2 b 6 Fig. 1 A flow network, with sources and sink t. The numbers next to the edges are the capacities.
g) Show the residual graph for the network flow given in answer to part (c). What is the bottleneck edge of the path (?, ?2, ?3, ?1, ?4, ?) in the residual graph you have given in answer to part (g) ? Show the network with the flow that results from augmenting the flow based on the path (?, ?2, ?3, ?1, ?4, ?) of the residual graph you have given in answer to part (g).
a) Show the residual graph for the network flow given in answer to part (c). b) What is the bottleneck edge of the path (?, ?3, ?4, ?) in the residual graph you have given in answer to part (d) ? c) Show the network with the flow that results from augmenting the flow based on the path (?, ?3, ?4, ?) of the residual graph you have given in answer to part (d).
What is a simple example of a network that has no bottleneck edges and is a valid flow network?
a) Show the residual graph for the network flow given in answer to part b) What is the bottleneck edge of the path (?, ?3, ?4, ?) in the residual graph you have given in answer to part (a) Show the network with the flow that results from augmenting the flow based on the path (?, ?3, ?4, ?) of the residual graph you have given in answer to part (a)
c.) Figure 2 shows a flow network on which an s-t flow has been computed. The capacity of each edge appears as a label next to the edge, and the numbers in boxes give the amount of flow sent on each edge. (Edges without boxed numbers have no flow being sent on them.) What is the value of the flow in Figure 2? Is this a maximum (s,t) flow in this graph? d). Find a maximum flow from s to t in Figure 2 (draw a picture like Figure 2, and specify the amount of flow in the box for each edge), and also say what its capacity is.