2log1-ε n hardness for the closest vector problem with preprocessing
SA Khot, P Popat, NK Vishnoi - Proceedings of the forty-fourth annual …, 2012 - dl.acm.org
SA Khot, P Popat, NK Vishnoi
Proceedings of the forty-fourth annual ACM symposium on Theory of computing, 2012•dl.acm.orgWe prove that for an arbitrarily small constant ε> 0, assuming NP⊈ DTIME (2logO 1-ε n), the
preprocessing versions of the closest vector problem and the nearest codeword problem are
hard to approximate within a factor better than 2log1-ε n. This improves upon the previous
hardness factor of (log n) δ for some δ> 0 due to [AKKV05].
preprocessing versions of the closest vector problem and the nearest codeword problem are
hard to approximate within a factor better than 2log1-ε n. This improves upon the previous
hardness factor of (log n) δ for some δ> 0 due to [AKKV05].
We prove that for an arbitrarily small constant ε>0, assuming NP⊈ DTIME (2logO 1-ε n), the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than 2log1-ε n. This improves upon the previous hardness factor of (log n)δ for some δ>0 due to [AKKV05].
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