Linear Degree Extractors and Inapproximability
        David Zuckerman
        U Texas

A randomness extractor is an algorithm which extracts randomness from a
low-quality random source, using some additional truly random bits.
Extractors have proved useful in a variety of seemingly unrelated areas.
We will introduce extractors and show a new construction, which  requires only
log n + O(1) additional random bits for sources with constant entropy  rate.

We use a related construction to show that approximating Max Clique and
Chromatic Number to within n^{1-epsilon} are NP-complete, for any  epsilon>0.
This derandomizes the results of Hastad and Feige-Kilian, who showed the
same inapproximability bounds but under randomized reductions.  We  can also
derandomize the results of Khot and show that approximating these  problems to
within certain n^{1-o(1)} factors are quasi-NP complete under quasi- polynomial
time reductions.