Before revision:  We show how an approximately shortest vector of certain lattice can be used to reduce the dimension of the problem, and how the oracle complexity of such a procedure is advantageous compared with the method that uses the Frank-Tardos framework .
After revision:  We show how an approximately shortest vector of certain lattice can be used to reduce the dimension of the problem, and how the oracle complexity of such a procedure is advantageous compared with the Gr\"otschel-Lov\'asz-Schrijver approach that uses simultaneous diophantine approximation .