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 Gr\"otschel-Lov\'asz-Schrijver approach that uses simultaneous diophantine approximation .
After revision:  We show how an approximately shortest vector of certain lattice can be used to effectively 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 .