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Computer networks should avoid single points of failure, that is, network vertices that can…

Computer networks should avoid single points of failure, that is, network vertices that can…

Computer networks should avoid single points of failure, that is, network vertices that can disconnect the network if they fail. We say an undirected, connected graph G is biconnected if it contains no vertex whose removal would divide G into two or more connected components. Give an algorithm for adding at most n edges to a connected graph G, with n ≥ 3 vertices and m ≥ n − 1 edges, to guarantee that G is biconnected. Your algorithm should run in O(n+m) time.