Approximation Algorithms for 3D Orthogonal Knapsack

We study non-overlapping axis-parallel packings of 3D boxes with profits into a dedicated bigger box where rotation is either forbidden or permitted, and we wish to maximize the total profit. Since this optimization problem is NP-hard, we focus on approximation algorithms. We obtain fast and simple...

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Bibliographic Details
Published in:Journal of computer science and technology Vol. 23; no. 5; pp. 749 - 762
Main Authors: Diedrich, Florian, Harren, Rolf, Jansen, Klaus, Thöle, Ralf, Thomas, Henning
Format: Journal Article
Language:English
Published: Boston Springer US 01.09.2008
Springer Nature B.V
Institute of Computer Science, University of Kiel, 24098 Kiel, Germany%Max-Planck-Institut fur Informatik, Campus E1 4, 66123 Saarbrucken, Germany%Department of Computer Science, ETH Zurich, Zurich, Switzerland
Subjects:
Algorithms
Approximation
Artificial Intelligence
Computer Science
Criteria
Data Structures and Information Theory
Information Systems Applications (incl.Internet)
Mathematical analysis
Optimization
Ratios
Regular Paper
Rotation
Software Engineering
Strip
Studies
Theory of Computation
Three dimensional
approximation algorithm
geometric configurations
computational and structural complexity
ISSN:1000-9000, 1860-4749
Online Access:Get full text
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Summary:We study non-overlapping axis-parallel packings of 3D boxes with profits into a dedicated bigger box where rotation is either forbidden or permitted, and 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 for the non-rotational scenario 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. Furthermore, we show how the used techniques can be adapted to the case where rotation by 90° either around the z -axis or around all axes is permitted, where we obtain algorithms with approximation ratios 6 + ϵ and 5 + ϵ, respectively. Finally our methods yield a 3D generalization of a packability criterion and a strip packing algorithm with absolute approximation ratio 29/4, improving the previously best known result of 45/4.
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ISSN:1000-9000
1860-4749
DOI:10.1007/s11390-008-9170-7