The flow-balance constraint associated with node 1 in the following network can be expressed as: -5 -10 5 -5 1 6 0 3 2 +10 4
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A: For solving your problem first of all we define Ford-Fulkerson Algorithm.Ford-Fulkerson Algorithm…
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A: Total number of paths = (5 − 1)!
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A: Option 3 is the correct answer
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A: Answer to the above question is in step2.
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A: According to my guideline I solve first three: a, b and c
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A: In the given network node between A and C node
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A: From S to T: Path S -> 3 -> 1 -> 7 -> t, Max Flow = 11 Path S -> 3 -> 1 -> 1…
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- For the graph shown below: a. Draw all the possible spanning trees. b. Draw the minimum spanning tree.Algorithm : (1. Single-destination Shortest Path, 2. Bellman-Ford, 3. Negative-Weight Cycles), Dynamic Programming, RNA Secondary Structure Consider n airports, labelled 1 through n. Each airport maintains a number of direct flights to other airports, represented by an edge with an associated cost. Since travel is currently restricted, one may only book direct flights—no airports will perform any transfers. However, things are beginning to open up again and airports are being slowly cleared to process transfers. These are done in order of label, so the first airport to allow transfers is 1, followed by 2, and so on. Once an airport is allowed to take transfers, flights through that airport may be booked. For example, consider the scenario depicted in Figure 1. When all airports are closed to transfers, flights may only be booked between airports connected by an edge. Thus, a flight from airport 5 to airport 2 may not be booked. However, once airport 1 is allowed to perform…Compute the maximum flow in the following flow network using Ford-Fulkerson's algorithm. 12 8 14 15 11 2 5 1 3 d 7 f 6 What is the maximum flow value? A minimum cut has exactly which vertices on one side? 4.
- What type of algorithm can be used to solve the basic network model for the critical path method? Label Setting Algorithm Dantzig's Algorithm Dijkstra's Algorithm Label Correcting AlgorithmFor each tumor, we can learn the size of the largest cell (in terms of area) using the "area_worst" column. Here are two plots that show "area_worst" broken out by whether the tumor was cancerous (M) or not (B). sb.histplot (data = cancer, x = "area_worst", hue = "Diagnosis") Count 120 Density 100 80 60 40 20 0- 0 ▸ sb.kdeplot(data = cancer, x = "area_worst", hue = "Diagnosis", fill = True --INSERT-- 0.0016 0.0014 0.0012 0.0010 0.0008- 0.0006 0.0004- 0.0002 0.0000 500 1000 1500 2000 2500 3000 3500 4000 area_worst 0 1000 2000 3000 Diagnosis M B area_worst 4000 Diagnosis M B 50003. Find the minimum spanning tree for the weighted graph below. Be sure to include the total cost, along with a picture of the spanning tree. 11 15 20 15 19 13 B 10. 18 7 12 10 00
- 2. Assume an interaction matrix with a minimum of 12 nodes. Demonstrate how the Kruskal algorithm can produce better results using the parallel approach.Mark Zuckerberg, the CEO of Facebook, has hired you to lead the Facebook Algorithms Group. He has asked you to use various graph algorithms to analyze the world's largest social network. The Facebook Graph has 2.8 billion vertices, with each vertex being a Facebook user. Two vertices are connected provided those two users are "friends". The first decision you need to make is how you want to model the Facebook graph. Determine whether you should use an adjacency-list representation or an adjacency-matrix representation.Dynamic ProgrammingConsider the following network below: (a) Label all of the nodes such that for every arc, (i,j), where i is the start and j the end node for the arc, the labels satisfy i < j.(b) Why can we use the node labeling algorithm to label the nodes in this network? (c) Use forward DP to find the shortest path from your first labeled node to every node in the network.(d) What fundamental characteristic of dynamic programs allow us to breakdown large-sized problems into a series of smaller-sized problems? What does this characteristic establishes?