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Approximate CVP_p in Time 2^{0.802 n}

Authors Friedrich Eisenbrand, Moritz Venzin

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Friedrich Eisenbrand
  • Ecole Polytechnique Fédérale de Lausanne, Switzerland
Moritz Venzin
  • Ecole Polytechnique Fédérale de Lausanne, Switzerland


The authors would like to thank the reviewers for their careful reviews and suggestions. The second author would like to thank Christoph Hunkenschröder, Noah Stephens-Davidowitz and Márton Naszódi for inspiring discussions.

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Friedrich Eisenbrand and Moritz Venzin. Approximate CVP_p in Time 2^{0.802 n}. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 43:1-43:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


We show that a constant factor approximation of the shortest and closest lattice vector problem w.r.t. any 𝓁_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. 𝓁₂. To obtain our result, we combine the latter algorithm w.r.t. 𝓁₂ with geometric insights related to coverings.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Randomness, geometry and discrete structures
  • Shortest and closest vector problem
  • approximation algorithm
  • sieving
  • covering convex bodies


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