Bin packing with fixed number of bins revisited

@article{Jansen2013BinPW,
  title={Bin packing with fixed number of bins revisited},
  author={Klaus Jansen and Stefan Kratsch and D{\'a}niel Marx and Ildik{\'o} Schlotter},
  journal={J. Comput. Syst. Sci.},
  year={2013},
  volume={79},
  pages={39-49}
}
As Bin Packing is NP-hard already for k = 2 bins, it is unlikely to be solvable in polynomial time even if the number of bins is a fixed constant. However, if the sizes of the items are polynomially bounded integers, then the problem can be solved in time n for an input of length n by dynamic programming. We show, by proving the W[1]hardness of Unary Bin Packing (where the sizes are given in unary encoding), that this running time cannot be improved to f(k) · n for any function f(k) (under… CONTINUE READING

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