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### Paper:

TR11-119 | 4th September 2011 22:42

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

TR11-119
Authors: Subhash Khot, Preyas Popat, Nisheeth Vishnoi
Publication: 11th September 2011 16:49
We prove that for an arbitrarily small constant $\eps>0,$ assuming NP$\not \subseteq$DTIME$(2^{{\log^{O(1/\epsilon)} n}})$, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than $2^{\log ^{1-\epsilon}n}.$ This improves upon the previous hardness factor of $(\log n)^\delta$ for some $\delta > 0$ due to \cite{Alekhnovich Khot Kindler Vishnoi 05}.