2. Consider a graph G(V,E), where is the set of nodes and E is the set of edges (links). For e E E, let we represent the

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2 Consider A Graph G V E Where Is The Set Of Nodes And E Is The Set Of Edges Links For E E E Let We Represent The 1 (178.17 KiB) Viewed 14 times

2. Consider a graph G(V,E), where is the set of nodes and E is the set of edges (links). For e E E, let we represent the weight of link e. Assume that each link weight corresponds to the probability that the link is operational and that the probability that a path is operational is given by the product of the weights of the links constituting the path. Your task is to find the most reliable path between each node pair. Assume that an implementation of the Dijkstra's algorithm that computes the least cost path (path with the smallest sum of weights) between any pair of nodes in the graph is available to you as a black box. You cannot make any changes in the given code. Describe how you can use the implementation of the Dijkstra's algorithm to compute the most reliable paths in the network, i.e., the path with the smallest product of weights between each node pair. Justify that your solution correctly computes the paths with the highest probability of operation as defined above.