Harmonic Algorithms for Packing d-Dimensional Cuboids into Bins

Sharma, E (2021) Harmonic Algorithms for Packing d-Dimensional Cuboids into Bins. In: 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, 15-17 Dec 2021, Virtual, Online.

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Abstract

We explore approximation algorithms for the d-dimensional geometric bin packing problem (dBP). Caprara 8 gave a harmonic-based algorithm for dBP having an asymptotic approximation ratio (AAR) of T�d-1 (where T� � 1.691). However, their algorithm doesn�t allow items to be rotated. This is in contrast to some common applications of dBP, like packing boxes into shipping containers. We give approximation algorithms for dBP when items can be orthogonally rotated about all or a subset of axes. We first give a fast and simple harmonic-based algorithm having AAR T�d . We next give a more sophisticated harmonic-based algorithm, which we call HGaPk, having AAR T�d-1(1 + ε). This gives an AAR of roughly 2.860+ε for 3BP with rotations, which improves upon the best-known AAR of 4.5. In addition, we study the multiple-choice bin packing problem that generalizes the rotational case. Here we are given n sets of d-dimensional cuboidal items and we have to choose exactly one item from each set and then pack the chosen items. Our algorithms also work for the multiple-choice bin packing problem. We also give fast and simple approximation algorithms for the multiple-choice versions of dD strip packing and dD geometric knapsack. © Eklavya Sharma.

Item Type:	Conference Paper
Publication:	Leibniz International Proceedings in Informatics, LIPIcs
Publisher:	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information:	The copyright for this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Keywords:	Geometry; Harmonic analysis, Approximation ratios; Asymptotic approximation; Bin packing; Bin packing problem; Geometric bin packing; Knapsacks; Multiple choice; Shipping containers; Simple++; Strip packing, Approximation algorithms
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	27 Jan 2022 11:47
Last Modified:	27 Jan 2022 11:47
URI:	http://eprints.iisc.ac.in/id/eprint/71040

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