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# Polynomial approximation schemes for smoothed and random instances of multidimensional packing problems

@inproceedings{Karger2007PolynomialAS, title={Polynomial approximation schemes for smoothed and random instances of multidimensional packing problems}, author={David R. Karger and Krzysztof Onak}, booktitle={SODA}, year={2007} }

- Published 2007 in SODA

The multidimensional bin packing and vector bin packing problems are known to not have asymptotic polynomial-time approximation schemes (unless P = NP). Nevertheless, we show that:
• Any smoothed (randomly perturbed) instance, and any instance from a class of other distributions, does have a polynomial-time probable approximation scheme. Namely, for any fixed ε > 0, we exhibit a linear-time algorithm that finds a (1+ ε)-approximate packing with probability 1 - 2-Ω(n) over the space of random… CONTINUE READING

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