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

Alberto Caprara,Andrea Lodi,Michele Monaci

doi:10.1016/j.disopt.2010.03.003

Alberto Caprara, Andrea Lodi + Show 1 more

https://doi.org/10.1016/j.disopt.2010.03.003

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Journal: Discrete Optimization	Publication Date: Apr 21, 2010
Citations: 12	License type: elsevier-specific: oa user license

Affiliation: University of Padua, University of Bologna

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.

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