# Approximating Bin Packing within O(log OPT * Log Log OPT) Bins

@article{Rothvoss2013ApproximatingBP, title={Approximating Bin Packing within O(log OPT * Log Log OPT) Bins}, author={Thomas Rothvoss}, journal={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, year={2013}, pages={20-29} }

For bin packing, the input consists of n items with sizes between 0 and 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(log2 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… CONTINUE READING

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