Hardness of Approximating the Closest Vector Problem with Pre-Processing

d Abstract] Mikhail Alekhnovich ∗ Subhash A. Khot † Guy Kindler ‡ Nisheeth K. Vishnoi § We show that, unless NP⊆DTIME(2poly log(n) ), the closest vector problem with pre-processing, for ℓp norm for any p ≥ 1, is hard to approximate within a factor of (log n)1/p−ǫ for any ǫ > 0. This improves the previous best factor of 31/p − ǫ due to Regev [19]. Our results also imply that under the same complexity assumption, the nearest codeword problem with pre-processing is hard to approximate within a factor of (log n)1−ǫ for any ǫ > 0.

• Type: Conference
• Year: 2005
• Where: FOCS
• Authors: Mikhail Alekhnovich, Subhash Khot, Guy Kindler, Nisheeth K. Vishnoi
• Keywords: Closest Vector Problem, FOCS 2005, Guy Kindler, Nearest Codeword Problem, Theoretical Computer Science