Hardness of approximation for orthogonal rectangle packing and covering problems

Chlebikova, Janka and Chlebik, M. (2009) Hardness of approximation for orthogonal rectangle packing and covering problems. Journal of Discrete Algorithms, 7 (3). pp. 291-305. ISSN 1570-8667 10.1016/j.jda.2009.02.002

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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
    Uncontrolled Keywords: inapproximability results orthogonal rectangle packing packing and covering with rotations rectangle covering
    Subjects: Computing
    Mathematics
    Departments/Research Groups: Faculty of Technology > School of Computing
    Related URLs:
    Depositing User: Janka Chlebikova
    Date Deposited: 29 Jun 2011 11:28
    Last Modified: 23 Jan 2014 07:32
    URI: http://eprints.port.ac.uk/id/eprint/3916

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