Several recent papers have established limits on the computational difficulty of lattice problems, focusing primarily on the `2 (Euclidean) norm. We demonstrate ...

We show that several recent "positive" results for lattice problems in the l 2 norm also hold in l p norms, for p>2. In particular, for lattices of dimension.

May 2, 2008 · Several recent papers have established limits on the computational difficulty of lattice problems, focusing primarily on the ℓ 2 (Euclidean) ...

Dec 3, 2006 · Abstract. We show that for any p ≥ 2, lattice problems in the `p norm are subject to all the same limits on hardness as are known for the `2 ...

Close Vector Problem (CVPγ). Approximation factor γ = γ(n), in some norm k·k. ▷ Given basis B and point v ∈ Rn, distinguish dist(v,L) ≤ 1 from dist(v,L) > γ.

Feb 15, 2007 · Abstract. We show that several recent “positive” results for lattice problems in the `2 norm also hold in `p norms, for any p > 2.

The results improve prior approximation factors for ℓp norms by up to up to $$\sqrt{n}$$ factors, and provide some evidence that lattice problems in ™p ...

J.-Y. CAI (1998). A relation of primal-dual lattices and the complexity of shortest lattice vector problem. Theor. Comput. Sci. 207(1), 105-116.

Sep 3, 2010 · This paper presents randomized reductions from the approximation versions of lattice problems in the ℓ2 norm to any norm ℓp where 1≤p≤∞. The ...

We show that several recent "positive" results for lattice problems in the \ell _2 norm also hold in \ell _p norms, for p \ge 2. In particular, for lattices ...