Approximate ${\mathrm{C}\mathrm{V}\mathrm{P}}_p$ in time $2^{0.802n}$

We show that a constant factor approximation of the shortest and closest lattice vector problem w.r.t. any ${\mathrm{\ell }}_p$-norm can be computed in time $2^{(0.802+ϵ)n}$. This matches the currently fastest constant factor approximation algorithm for the shortest vector problem w.r.t. ${\mathrm{\ell }}_2$. To obtain our result, we combine the latter algorithm w.r.t. ${\mathrm{\ell }}_2$ with geometric insights related to coverings.