Prove that if there is a polynomial time approximation algorithm for the maximum clique problem that has approximation ratio 1000 then there is a polynomial time approximation algorithm with approximation ratio 1.000000001. This is actually a slightly easier problem than problem 35-2 part b in the CLRS text, which I suggest that you look at for inspiration. Note that in some sense this can be viewed as a gap reduction Prove that if there is a polynomial time approximation algorithm for the maximum clique problem that has approximation ratio 1000 then there is a polynomial time approximation algorithm with approximation ratio 1.000000001. This is actually a slightly easier problem than problem 35-2 part b in the CLRS text, which I suggest that you look at for inspiration. Note that in some sense this can be viewed as a gap reduction