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http://dx.doi.org/10.7232/JKIIE.2012.38.1.001

Hardness of Approximation for Two-Dimensional Vector Packing Problem with Large Items  

Hwang, Hark-Chin (Department of Industrial Engineering, Chosun University)
Kang, Jang-Ha (Department of Industrial Engineering, Chosun University)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.38, no.1, 2012 , pp. 1-6 More about this Journal
Abstract
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.
Keywords
Two-Dimensional Vector Packing; Algorithm; Complexity;
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