English

Approximate $\mathrm{CVP}_{p}$ in time $2^{0.802 \, n}$

Computational Geometry 2020-06-17 v2 Data Structures and Algorithms

Abstract

We show that a constant factor approximation of the shortest and closest lattice vector problem w.r.t. any p\ell_p-norm can be computed in time 2(0.802+ϵ)n2^{(0.802 +{\epsilon})\, n}. This matches the currently fastest constant factor approximation algorithm for the shortest vector problem w.r.t. 2\ell_2. To obtain our result, we combine the latter algorithm w.r.t. 2\ell_2 with geometric insights related to coverings.

Cite

@article{arxiv.2005.04957,
  title  = {Approximate $\mathrm{CVP}_{p}$ in time $2^{0.802 \, n}$},
  author = {Friedrich Eisenbrand and Moritz Venzin},
  journal= {arXiv preprint arXiv:2005.04957},
  year   = {2020}
}

Comments

We improved the introduction and added the case $p \in [1,2)$

R2 v1 2026-06-23T15:26:59.992Z