Irit Dinur, S. Safra

The label-cover problem was introduced in \cite{ABSS} and shown

there to be quasi-NP-hard to approximate to within a factor of

$2^{\log^{1-\delta}n}$ for any {\em constant} $\delta>0$. This

combinatorial graph problem has been utilized \cite{ABSS,GM,ABMP}

for showing hardness-of-approximation of numerous problems. We

present a direct combinatorial reduction from low

error-probability PCP ...
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Irit Dinur

This paper shows SVP_\infty and CVP_\infty to be NP-hard to approximate

to within any factor up to $n^{1/\log\log n}$. This improves on the

best previous result \cite{ABSS} that showed quasi-NP-hardness for

smaller factors, namely $2^{\log^{1-\epsilon}n}$ for any constant

$\epsilon>0$. We show a direct reduction from SAT to these

problems, that ...
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