  The Restricted Assignment Problem is a prominent special case of Scheduling
on Parallel Unrelated Machines. For the strongest known linear programming
relaxation, the configuration LP, we improve the non-constructive bound on its
integrality gap from 1.9142 to 1.8334 and significantly simplify the proof.
Then we give a constructive variant, yielding a 1.8334-approximation in
quasi-polynomial time. This is the first quasi-polynomial algorithm for this
problem improving on the long-standing approximation rate of 2.
