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

Authors:
Alberto Caprara;Andrea Lodi;Michele Monaci
Affiliations:
DEIS, Universití di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy;DEIS, Universití di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy;DEI, Universití di Padova, Via Gradenigo 6/A, I-35131 Padova, Italy
Venue:
Discrete Optimization
Year:
2010

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Abstract

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 other hand, getting rid of the additive constant to achieve a canonical approximation scheme appears to be widely nontrivial.