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Hardness of Approximating the Closest Vector Problem with Pre-Processing

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Abstract

We show that the pre-processing versions of the closest vector problem and the nearest codeword problem are \({\mathsf {NP}}\) -hard to approximate within any constant factor.

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Authors and Affiliations

  1. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Mikhail Alekhnovich

  2. Computer Science Department, Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    Subhash A. Khot

  3. School of Computer Science and Engineering, The Hebrew University of Jerusalem, Ross Building, Givat Ram Campus, 91904, Jerusalem, Israel

    Guy Kindler

  4. Microsoft Research India, 196/36 2nd Main Sadashivnagar, Bangalore, 560080, India

    Nisheeth K. Vishnoi

Authors
  1. Mikhail Alekhnovich
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  2. Subhash A. Khot
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  3. Guy Kindler
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  4. Nisheeth K. Vishnoi
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Correspondence to Nisheeth K. Vishnoi.

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Alekhnovich, M., Khot, S.A., Kindler, G. et al. Hardness of Approximating the Closest Vector Problem with Pre-Processing. comput. complex. 20, 741–753 (2011). https://doi.org/10.1007/s00037-011-0031-3

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  • DOI: https://doi.org/10.1007/s00037-011-0031-3

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