Problem 2. Apply Dijkstra's least-cost or shorted-path algorithm to the network shown on the right. Complete...
Question 5 (5 points) Apply Dijkstra's Algorithm to the following graph, computing the shortest path for al vertices from vertex A. Present the results after each vertex has been processed 3 20 B 47 20 You may wish to present the results in the format of the following table: Stage Current Vertex Labels and Distances A 0 A 0 D 231 A 213 E 4 F21 A 90 Each row states (a) the current stage, (b) the vertex just added...
Consider the network shown below. Use Dijkstra's algorithm to find the shortest paths from node a to all other nodes. Enter your answers in the a shortest path answers in the following format: node-node-node. For example, if the ssignment link. Enter the shortest path from a to c is through node b, you would enter the answer as: a-b-c 3 5 6 6
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...
12 8 4 6 4 6 2. Consider the same network as in Problem 1. Assume node r is the only destination in the network. Use a table to show the computation process of the Bellman-Ford algorithm. Each row in the table corresponds to one iteration of the algorithm, and each column is a pair (D (A), H(A)) where D,(A) is the cost from node i to A and Hi(A) is the next hop on the path from i to...
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...
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...
Run the Dijkstra’s algorithm on the directed graph of the following figure 24.6, using vertex t as the source. In the style of Figure 24.6, show the d and ? values and the vertices in set S after each iteration of the while loop. 1 8 10 I 10 14 4 6 4 6 2 3 2 3 4 6 5 5 2 (a) (c) 1 10 13 4 6 (d) (e) Figure 24.6 The execution of Dijkstra's algorithm. The...
5. If we apply binary dilation to the same large object twice using the same small structuring element, the effect, if any, of the second dilation on the object is that the object: (a) is unchanged (b) is completely removed (c) becomes larger (d) becomes smaller (e) does not change 6. Which of the following is/are true? (a) Dijkstra's algorithm can be used to find shortest paths in a network (b) Dijkstra's algorithm is a method to find straight lines...
2. Apply Dijkstra’s algorithm as discussed in class to solve the single-source shortest-paths problem for the following graph. Consider node a to be the source. (10 points) a. Show the completed table. b. State the shortest path from A to J and state its length. c. State the shortest path from A to K and state its length. d. State the shortest path from A to L and state its length. 3 5 6 4 3 2 1 2. d...
Problem 2 A transportation network is shown in the attached figure. Perform traffic assignment for a demand of 3000 vehicles from zone 3 to zone 5 as follows: (1) Find the shortest path between these two zones using the minimum path algorithm discussed in class, and assign 50% of the traffic to the path. (2) Update the travel time for each links with a traffic load by a factor of 1.2 (ie, 20% increase) and assign another 50% of the...