Hardness of Approximating the Closest Vector Problem with Pre-Processing

Authors:
Mikhail Alekhnovich;Subhash A. Khot;Guy Kindler;Nisheeth K. Vishnoi
Affiliations:
Institute for Advanced Study, 08540, Princeton, NJ, USA;New York University, Computer Science Department, Courant Institute of Mathematical Sciences, 10012, New York, NY, USA;The Hebrew University of Jerusalem, School of Computer Science and Engineering, Ross Building, Givat Ram Campus, 91904, Jerusalem, Israel;Microsoft Research India, 196/36 2nd Main Sadashivnagar, 560080, Bangalore, India
Venue:
Computational Complexity - Special issue in memory of Misha Alekhnovich
Year:
2011

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2log1-ε n hardness for the closest vector problem with preprocessing

STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing

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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.