• Journal of Korean Institute of Industrial Engineers
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• v.38 no.1
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• pp.1-6
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• 2012

We consider a two-dimensional vector packing problem in which each item has size in x- and y-coordinates. The purpose of this paper is to provide a ground work on how hard two-dimensional vector packing problems are for large items. We prove that the problem with each item greater than 1/2-${\varepsilon}$ either in x- or y-coordinates for 0 < ${\varepsilon}$ ${\leq}$ 1/6 has no APTAS unless P = NP.