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# An approximation scheme for the two-stage, two-dimensional knapsack problem

@article{Caprara2010AnAS, title={An approximation scheme for the two-stage, two-dimensional knapsack problem}, author={Alberto Caprara and Andrea Lodi and Michele Monaci}, journal={Discrete Optimization}, year={2010}, volume={7}, pages={114-124} }

- Published 2010 in Discrete Optimization
DOI:10.1016/j.disopt.2010.03.003

We present an approximation scheme for the two-dimensional version of the knapsack problem which requires packing a maximum-area set of rectangles in a unit square bin, with the further restrictions that packing must be orthogonal without rotations and done in two stages. Achieving a solution which is close to the optimum modulo a small additive constant can be done by taking wide inspiration from an existing asymptotic approximation scheme for two-stage two-dimensional bin packing. On the… CONTINUE READING