A network is given as follows, where the numbers on arcs are the unit costs. Find the shortest paths from node 0 to all other nodes by Dijkstra's algorithm. (No point will be given if steps of Dijkstra's algorithm are shown.) 1 2 1 6. 2 12 2. Find the maximum flow from node 1 to node 5. (All numbers on arcs are the capacities.) Use max-flow/min-cut theorem to support your solution. 3 3 3. 2.

A network is given as follows, where the numbers on arcs are the unit costs. Find the shortest paths from node 0 to all other nodes by Dijkstra's algorithm. (No point will be given if steps of Dijkstra's algorithm are shown.) 1 2 1 6. 2 12 2. Find the maximum flow from node 1 to node 5. (All numbers on arcs are the capacities.) Use max-flow/min-cut theorem to support your solution. 3 3 3. 2.

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Q1. The network in Figure 1 gives distance in miles between pairs of cities 1,2,… and 8. Use Dijkstra’s algorithm to find the shortest route between following cities. Solve the problems using Floyd’s Algorithm as well. a) Cities 1 and 8 b) Cities 2 and 6
Outline the Ford and Fulkerson's algorithm. Prove that if the capacities are integers, then this algorithm correctly computes a maximum flow.
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…
Show the final flow that the Ford-Fulkerson Algorithm finds for this network, given that it proceeds to completion from the flow rates you have given in your answer to part, and augments flow along the edges (?,?1,?3,?) and (?,?2,?5,?). Identify a cut of the network that has a cut capacity equal to the maximum flow of the network.
Problem 2: Compute the shortest path from s to t in the following network using the Bellman-Ford algorithm. 2 (² 5 3 2 1 -2 2 -1 (3 t -4
How do I find the minimum capacity of an s-t cut in this flow network?
4. Graph Theory and Approximation Algorithms- (a) Find the maximum flow possible from vertex s to vertex t in the given graph. Show all your steps Given an example to show why reverse flow edges should be included to get the optimal flow 12 vi V4 20 16 8 4 9. 14 V3 v2 15 (b) Given below are the distances between A, B, C, D, E, F. You have to start from A, visit all the vertices and return back to the A. Find the optimal path using the approximation algorithm discussed in class. Show all your steps. () | A BC D E F A0 4 4 3 5 5 в| 4 0 2 4 C 4 2 D 3 4 E 5 3 6 F 5 3 4 3 3 6. 4 5 4 5 4 5 5 0 in