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Approximate CVP_p in Time 2^{0.802 n}

Authors Friedrich Eisenbrand, Moritz Venzin

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Subject Classification

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

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Abstract

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ESA.2020.43

Author Details

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

Funding

The authors acknowledge support from the Swiss National Science Foundation within the project Lattice Algorithms and Integer Programming (Nr. 200021-185030).

Acknowledgements

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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