Polynomiality for Bin Packing with a Constant Number of Item Types

@inproceedings{Goemans2014PolynomialityFB,
  title={Polynomiality for Bin Packing with a Constant Number of Item Types},
  author={Michel X. Goemans and Thomas Rothvoss},
  booktitle={SODA},
  year={2014}
}
We consider the bin packing problem with d different item sizes s_i and item multiplicities a_i, where all numbers are given in binary encoding. This problem formulation is also known as the 1-dimensional cutting stock problem. In this work, we provide an algorithm which, for constant d, solves bin packing in polynomial time. This was an open problem for all d >= 3. In fact, for constant d our algorithm solves the following problem in polynomial time: given two d-dimensional polytopes P and Q… 

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