Euclidean SVP is deterministically NP-hard to approximate within any constant factor

Abstract

We prove that, for every constant $\rho >1$, the Euclidean shortest vector problem is NP-hard to approximate within any constant factor $\rho$ under a deterministic polynomial-time many-one reduction. This extends our previous deterministic NP-hardness result from $\rho <\sqrt{2}$ to arbitrary constants and gives a deterministic version of Khot's randomized arbitrary-constant theorem.

27 pages, major revision