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Cutting Stock with Rotation: Packing Square Items into Square Bins

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Combinatorial Optimization and Applications (COCOA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12577))

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Abstract

In the square packing problem, the goal is to place a multi-set of square-items of various sizes into a minimum number of square-bins of equal size. Items are assumed to have various side-lengths of at most 1, and bins have uniform side-length 1. Despite being studied previously, the existing models for the problem do not allow rotation of items. In this paper, we consider the square packing problem in the presence of rotation. As expected, we can show that the problem is NP-hard. We study the problem under a resource augmented setting where an approximation algorithm can use bins of size \(1+\alpha \), for some \(\alpha >0\), while the algorithm’s packing is compared to an optimal packing into bins of size 1. Under this setting, we show that the problem admits an asymptotic polynomial time scheme (APTAS) whose solutions can be encoded in a poly-logarithmic number of bits.

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Authors and Affiliations

  1. Department of Computer Science, University of Manitoba, Winnipeg, Canada

    Shahin Kamali & Pooya Nikbakht

Authors
  1. Shahin Kamali
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  2. Pooya Nikbakht
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Correspondence to Shahin Kamali or Pooya Nikbakht .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Xiamen University, Xiamen, China

    Zhongnan Zhang

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Kamali, S., Nikbakht, P. (2020). Cutting Stock with Rotation: Packing Square Items into Square Bins. In: Wu, W., Zhang, Z. (eds) Combinatorial Optimization and Applications. COCOA 2020. Lecture Notes in Computer Science(), vol 12577. Springer, Cham. https://doi.org/10.1007/978-3-030-64843-5_36

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  • DOI: https://doi.org/10.1007/978-3-030-64843-5_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-64842-8

  • Online ISBN: 978-3-030-64843-5

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