Hardness of approximation for orthogonal rectagle packing and covering problems

Chlebík, Miroslav and Chlebíková, Janka (2009) Hardness of approximation for orthogonal rectagle packing and covering problems. Journal of Discrete Algorithms, 7 (3). pp. 291-305. ISSN 1570-8667

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Abstract

Bansal and Sviridenko [N. Bansal, M. Sviridenko, New approximability and inapproximability results for 2-dimensional bin packing, in: Proceedings of the 15th Annual ACM¿SIAM Symposium on Discrete Algorithms, SODA, 2004, pp. 189¿196] proved that there is no asymptotic PTAS for 2-dimensional Orthogonal Bin Packing (without rotations), unless P=NP. We show that similar approximation hardness results hold for several 2- and 3-dimensional rectangle packing and covering problems even if rotations by ninety degrees are allowed. Moreover, for some of these problems we provide explicit lower bounds on asymptotic approximation ratio of any polynomial time approximation algorithm. Our hardness results apply to the most studied case of 2-dimensional problems with unit square bins, and for 3-dimensional strip packing and covering problems with a strip of unit square base.

Item Type: Article
Divisions: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Miroslav Chlebik
Date Deposited: 06 Feb 2012 18:36
Last Modified: 03 Apr 2012 14:14
URI: http://sro.sussex.ac.uk/id/eprint/17330

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