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Approximation Algorithms for 3D Orthogonal Knapsack

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Theory and Applications of Models of Computation (TAMC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4484))

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Abstract

We study non-overlapping axis-parallel packings of 3D boxes with profits into a dedicated bigger box where rotation is forbidden; we wish to maximize the total profit. Since this optimization problem is NP-hard, we focus on approximation algorithms. We obtain fast and simple algorithms with approximation ratios 9 + ε and 8 + ε as well as an algorithm with approximation ratio 7 + ε that uses more sophisticated techniques; these are the smallest approximation ratios known for this problem. Topics: Algorithms, computational and structural complexity.

Research supported in part by DFG Project, “Entwicklung und Analyse von Approximativen Algorithmen für Gemischte und Verallgemeinerte Packungs- und Überdeckungsprobleme, JA 612/10-1”, in part by the German Academic Exchange Service DAAD, in part by project AEOLUS, EU contract number 015964, and in part by a grant “DAAD Doktorandenstipendium” of the German Academic Exchange Service DAAD. Part of this work was done while visiting the ID-IMAG, ENSIMAG, Grenoble.

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Authors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Olshausenstr. 40, 24098 Kiel, Germany

    Florian Diedrich, Klaus Jansen, Ralf Thöle & Henning Thomas

  2. Fachbereich Informatik, Universität Dortmund, Otto-Hahn-Str. 14, 44227 Dortmund, Germany

    Rolf Harren

Authors
  1. Florian Diedrich
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  2. Rolf Harren
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  3. Klaus Jansen
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  4. Ralf Thöle
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  5. Henning Thomas
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Editor information

Jin-Yi Cai S. Barry Cooper Hong Zhu

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© 2007 Springer-Verlag Berlin Heidelberg

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Diedrich, F., Harren, R., Jansen, K., Thöle, R., Thomas, H. (2007). Approximation Algorithms for 3D Orthogonal Knapsack. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_3

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  • DOI: https://doi.org/10.1007/978-3-540-72504-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72503-9

  • Online ISBN: 978-3-540-72504-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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