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Given an undirected graph \( G = (V, E) \), a vertex cover is a subset of \( V \) so that every edge in \( E \) has at least one endpoint in the vertex cover. The problem of finding a minimum vertex cover is to find a vertex cover of the smallest possible size. Formulate this problem as an integer linear programming problem.

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a) write the algorithm b) Briefly explain why the algorithm solves the problem, and the correctness c ) State and briefly explain the running time of your algorithm
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