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 ... more >>>

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 ... more >>>