Approximating-CVP to Within Almost-Polynomial Factors is NP-Hard

  title={Approximating-CVP to Within Almost-Polynomial Factors is NP-Hard},
  author={Irit Dinur and Guy Kindler and Shmuel Safra},
This paper shows the closest vector in a lattice to be NPhard to approximate to within any factor up to 2(logn)1 where = (log logn) c for any constant c < 12 . Introduction A latticeL = L(v1; ::; vn), for vectorsv1; ::; vn 2 Rn is the set of all integer linear combinations of v1; ::; vn, that is, L = fP aivi j ai 2 Zg. Given a latticeL and an arbitrary… CONTINUE READING