Suppose n computers in a wired local-area network are arranged in a tree, T, which is rooted at one of these computers (say, one that is connected to the Internet). That is, the computers in this network form the nodes of T, and the edges of T are determined by the pairs of computers that have cables connecting them to each other. The administrator of this network is concerned about reliability and wants to buy some network monitoring devices to continuously check the quality of the connections in T. If such a monitoring device is installed on a computer, x, then x is able to continuously monitor all the direct connections that x has with other computers. To save money, he is asking that you determine the fewest number of monitoring devices needed in order to have at least one device monitoring every connection in T. For example, if every computer in T other than the root were a child of the root, then the administrator would need only one monitoring device (placed at the root). Describe an efficient algorithm for solving this problem, which is known as the vertex-cover problem, for T. What is the running time of your algorithm?