1. For the network topology given in Fig. 1, give distance-vector table for nodes A and E. A O- | 5 | D 5 B 1 4 | 3 E 3 6 C O | 2 F Fig. 1: Network for Problem 1.
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- If P ≠ NP then there does not exist a minimal-time solution to FSSP for the network topology introduced below as Variation the direct three-dimensional analogue of Kobayashi’s Variation.Subject: DLD Simplify the following function using K-map F(W,X,Y,Z) = (1,2,4,6,8,9,10,11,14,15) G(W,X,Y,Z) = Product(2,3,6,8)+d(1,4,7,10,12,13,15)Construct an undirected network diagram using the given set of nodes and arcs, also find the shortest path and distance from node A to node E using Dijkstra’s algorithm. Nodes {A, B, C, D, E} Arcs {(AB)=2, (AC)=3, (BC)=2, (CD)=1, (DB)=2, (DE)=1, (CE)=6}
- i. How can a mixed network be converted into a directed network? ii. Distinguish between the various types of arcs in network model iii. In one sentence carefully distinguish between feasible solution and optimal solutionQuestion 18 .The following weighted graph corresponds to a railway network, determine the shortest way from station a to zGiven the following nodes from A to G as shown in the diagram, determine the shortest path network from node A to all other nodes in the given cost network graph.
- Consider the Omega network and Butterfly network from p nodes in the leftmost column to p nodes in the rightmost column for some p=2^k. The Omega network is defined in Chapter 2 of the text book such that Si is connected to element S j if j=2i for or j=2i+1-p for See Chapter 2 in text book for its definition. The Butterfly network is an interconnection network composed of log p levels (as the omega network). In a Butterfly network, each switching node i at a level l is connected to the identically numbered element at level l + 1 and to a switching node whose number differs from itself only at the lth most significant bit. Therefore, switching node Si is connected to element S j at level l if j = i or j . Prove that for each node Si in the leftmost column and a node Sj in the rightmost column, there is a path from Si to Sj in the Omega network. Prove that for each node Si in the leftmost and a node Sj in the rightmost, there is a path from Si to Sj in the Butterfly network.Consider the following network: a.) Find the shortest path from node 1 to node 8 using Dijkstra’s algorithm. Write the length of the shortest path as well as the edges that compose it. b.) Write an integer programming formulation to find the second-shortest path from 1 to 8 in this network. (Hint: if the shortest path is not available, the second-shortest path becomes the shortest path.)Describe how to construct an incremental network in the Ford-Fulkerson algorithm in order to find the maximal flow through a network flow model with minimal overall cost.
- Network Routing Analysis - Algorithms Consider the following network. With the indicated link costs, use Dijkstra’sshortest-path algorithm to compute the shortest path from x to all network nodes.Show how the algorithm works by computing a table similar to Table 4.3.Computer Science Hand-execute the Ford-Fulkerson algorithm on the transport network. Find the maximum flow through the network. Identify the cut whose capacity equals the maximum flow. Your answer should include all the details of the execution clearly.As we all know, heuristic or approximation algorithms may not always provide the best solution to a problem, but they are very efficient in terms of polynomial time. (a) Propose an approximation method for the travelling salesman problem (TSP) and analyze the time complexity and limitations of the proposed approach. (2) Provide two examples of inputs for which the method in (a) produces the best and not-the best answers, respectively. (3) There should be between six and eight nodes in each network.