We show that a constant factor approximation of the shortest and closest lattice vector problem w.r.t. \ell_{\infty can be computed in time 2^{(0.802 +{\epsilon})\, n}. This is breaking thekissing number barrier of 3^n that is inherent in the previous best approaches tackling this problem . We obtain this improvement by incorporating a bound on the number of scaled hypercubes that are necessary to cover the \ell_2-ball of radius \sqrt{n \ell_2. It is to pick the smallest pairwise difference w.r.t. \ell _{\infty .
We show that a constant factor approximation of the shortest and closest lattice vector problem w.r.t. any \ell_p-norm can be computed in time 2^{(0.802 +{\epsilon})\, n}. This matches the currently fastest constant factor approximation algorithm for the shortest vector problem w.r.t. \ell_2. To obtain our result, we combine the latter algorithm w.r.t. \ell _2 with geometric insights related to coverings .
R
\ell_{\infty
any \ell_p-norm
D
is breaking the
D
kissing number barrier
R
of 3^n that is inherent in the previous best approaches tackling this problem . We obtain this improvement by incorporating a bound on the number of scaled hypercubes that are necessary to cover the \ell_2-ball of radius \sqrt{n
matches the currently fastest constant factor approximation algorithm for the shortest vector problem w.r.t.
R
It is to pick the smallest pairwise difference
To obtain our result, we combine the latter algorithm
R
_{\infty
_2 with geometric insights related to coverings