Question: 1. [10 marks] Recall that in a graph G (V, E) a set U C V is an independent set iff V-U is a vertex

1. [10 marks] Recall that in a graph G (V, E)

1. [10 marks] Recall that in a graph G (V, E) a set U C V is an independent set iff V-U is a vertex cover. Also, U is an independent set in G iff U is a clique in the complement of G. These relationships provide polynomial time reductions among these three NP-complete problems The point of this question is to ask whether these reductions preserve good approximations. (a) [5 marks] Does a polynomial time constant factor approximation algorithm for the Inde- pendent Set Problem give a polynomial time constant factor approximation algorithm or the Clique Problem? Explain (b) 5 marks] Does a polynomial time constant factor approximation algorithm for the Inde- pendent Set Problem give a polynomial time constant factor approximation algorithnm for the Vertex Cover Problem? Explain

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