$2^{\log^{1-\eps} n}$ Hardness for Closest Vector Problem with Preprocessing

Subhash Khot; Preyas Popat; Nisheeth K. Vishnoi

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arXiv · 1109.2176

$2^{\log^{1-\eps} n}$ Hardness for Closest Vector Problem with Preprocessing

Subhash Khot·Preyas Popat·Nisheeth K. Vishnoi

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Abstract

We prove that for an arbitrarily small constant $\eps>0,$ assuming NP$\not \subseteq$DTIME$(2^{{\log^{O(1/\eps)} n}})$, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than $2^{\log ^{1-\eps}n}.$ This improves upon the previous hardness factor of $(\log n)^\delta$ for some $\delta > 0$ due to \cite{AKKV05}.

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Subhash Khot, Preyas Popat, Nisheeth K. Vishnoi. 2011-09-10. $2^{\log^{1-\eps} n}$ Hardness for Closest Vector Problem with Preprocessing. https://arxiv.org/abs/1109.2176

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