  For bin packing, the input consists of n items with sizes s_1,...,s_n in
[0,1] which have to be assigned to a minimum number of bins of size 1. The
seminal Karmarkar-Karp algorithm from '82 produces a solution with at most OPT
+ O(log^2 OPT) bins.
  We provide the first improvement in now 3 decades and show that one can find
a solution of cost OPT + O(log OPT * log log OPT) in polynomial time. This is
achieved by rounding a fractional solution to the Gilmore-Gomory LP relaxation
using the Entropy Method from discrepancy theory. The result is constructive
via algorithms of Bansal and Lovett-Meka.
