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Approximate $\mathrm{CVP}_{p}$ in time $2^{0.802 \, n}$ (2005.04957v2)
Published 11 May 2020 in cs.CG and cs.DS
Abstract: 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.