Better Bin Packing Approximations via Discrepancy Theory

SIAM J. Comput., Volume 45, Issue 3, 2016, Pages 930-946.

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Abstract:

For bin packing, the input consists of $n$ items with sizes $s_1,ldots,s_n [0,1]$ which have to be assigned to a minimum number of bins of size 1. The seminal Karmarkar--Karp algorithm from 1982 produces a solution with at most $OPT + O(log^2 OPT)$ bins. We provide the first improvement in over three decades and show that one can find a ...More

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