Improved Approximation Algorithms for Three-Dimensional Bin Packing
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| Titel: | Improved Approximation Algorithms for Three-Dimensional Bin Packing |
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| Autoren: | Kar, Debajyoti, Khan, Arindam, Rau, Malin, 1990 |
| Quelle: | 52nd EATCS International Colloquium on Automata, Languages, and Programming, ICALP 2025, Aarhus, Denmark Leibniz International Proceedings in Informatics, LIPIcs. 334 |
| Schlagwörter: | Geometric Packing, Approximation Algorithms, Multidimensional Packing |
| Beschreibung: | We study three fundamental three-dimensional (3D) geometric packing problems: 3D (Geometric) Bin Packing (3d-bp), 3D Strip Packing (3d-sp), and Minimum Volume Bounding Box (3d-mvbb), where given a set of 3D (rectangular) cuboids, the goal is to find an axis-aligned nonoverlapping packing of all cuboids. In 3d-bp, we need to pack the given cuboids into the minimum number of unit cube bins. In 3d-sp, we need to pack them into a 3D cuboid with a unit square base and minimum height. Finally, in 3d-mvbb, the goal is to pack into a cuboid box of minimum volume. It is NP-hard to even decide whether a set of rectangles can be packed into a unit square bin - giving an (absolute) approximation hardness of 2 for 3d-bp and 3d-sp. The previous best (absolute) approximation for all three problems is by Li and Cheng (SICOMP, 1990), who gave algorithms with approximation ratios of 13, 46/7, and 46/7 + ε, respectively, for 3d-bp, 3d-sp, and 3d-mvbb. We provide improved approximation ratios of 6, 6, and 3 + ε, respectively, for the three problems, for any constant ε > 0. For 3d-bp, in the asymptotic regime, Bansal, Correa, Kenyon, and Sviridenko (Math. Oper. Res., 2006) showed that there is no asymptotic polynomial-time approximation scheme (APTAS) even when all items have the same height. Caprara (Math. Oper. Res., 2008) gave an asymptotic approximation ratio of T∞ 2 + ε ≈ 2.86, where T∞ is the well-known Harmonic constant in Bin Packing. We provide an algorithm with an improved asymptotic approximation ratio of 3T∞/2 + ε ≈ 2.54. Further, we show that unlike 3d-bp (and 3d-sp), 3d-mvbb admits an APTAS. |
| Dateibeschreibung: | electronic |
| Zugangs-URL: | https://research.chalmers.se/publication/547453 https://research.chalmers.se/publication/547453/file/547453_Fulltext.pdf |
| Datenbank: | SwePub |
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| Items | – Name: Title Label: Title Group: Ti Data: Improved Approximation Algorithms for Three-Dimensional Bin Packing – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kar%2C+Debajyoti%22">Kar, Debajyoti</searchLink><br /><searchLink fieldCode="AR" term="%22Khan%2C+Arindam%22">Khan, Arindam</searchLink><br /><searchLink fieldCode="AR" term="%22Rau%2C+Malin%22">Rau, Malin</searchLink>, 1990 – Name: TitleSource Label: Source Group: Src Data: <i>52nd EATCS International Colloquium on Automata, Languages, and Programming, ICALP 2025, Aarhus, Denmark Leibniz International Proceedings in Informatics, LIPIcs</i>. 334 – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Geometric+Packing%22">Geometric Packing</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+Algorithms%22">Approximation Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Multidimensional+Packing%22">Multidimensional Packing</searchLink> – Name: Abstract Label: Description Group: Ab Data: We study three fundamental three-dimensional (3D) geometric packing problems: 3D (Geometric) Bin Packing (3d-bp), 3D Strip Packing (3d-sp), and Minimum Volume Bounding Box (3d-mvbb), where given a set of 3D (rectangular) cuboids, the goal is to find an axis-aligned nonoverlapping packing of all cuboids. In 3d-bp, we need to pack the given cuboids into the minimum number of unit cube bins. In 3d-sp, we need to pack them into a 3D cuboid with a unit square base and minimum height. Finally, in 3d-mvbb, the goal is to pack into a cuboid box of minimum volume. It is NP-hard to even decide whether a set of rectangles can be packed into a unit square bin - giving an (absolute) approximation hardness of 2 for 3d-bp and 3d-sp. The previous best (absolute) approximation for all three problems is by Li and Cheng (SICOMP, 1990), who gave algorithms with approximation ratios of 13, 46/7, and 46/7 + ε, respectively, for 3d-bp, 3d-sp, and 3d-mvbb. We provide improved approximation ratios of 6, 6, and 3 + ε, respectively, for the three problems, for any constant ε > 0. For 3d-bp, in the asymptotic regime, Bansal, Correa, Kenyon, and Sviridenko (Math. Oper. Res., 2006) showed that there is no asymptotic polynomial-time approximation scheme (APTAS) even when all items have the same height. Caprara (Math. Oper. Res., 2008) gave an asymptotic approximation ratio of T∞ 2 + ε ≈ 2.86, where T∞ is the well-known Harmonic constant in Bin Packing. We provide an algorithm with an improved asymptotic approximation ratio of 3T∞/2 + ε ≈ 2.54. Further, we show that unlike 3d-bp (and 3d-sp), 3d-mvbb admits an APTAS. – Name: Format Label: File Description Group: SrcInfo Data: electronic – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="https://research.chalmers.se/publication/547453" linkWindow="_blank">https://research.chalmers.se/publication/547453</link><br /><link linkTarget="URL" linkTerm="https://research.chalmers.se/publication/547453/file/547453_Fulltext.pdf" linkWindow="_blank">https://research.chalmers.se/publication/547453/file/547453_Fulltext.pdf</link> |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.4230/LIPIcs.ICALP.2025.104 Languages: – Text: English Subjects: – SubjectFull: Geometric Packing Type: general – SubjectFull: Approximation Algorithms Type: general – SubjectFull: Multidimensional Packing Type: general Titles: – TitleFull: Improved Approximation Algorithms for Three-Dimensional Bin Packing Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kar, Debajyoti – PersonEntity: Name: NameFull: Khan, Arindam – PersonEntity: Name: NameFull: Rau, Malin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 18688969 – Type: issn-locals Value: SWEPUB_FREE – Type: issn-locals Value: CTH_SWEPUB Numbering: – Type: volume Value: 334 Titles: – TitleFull: 52nd EATCS International Colloquium on Automata, Languages, and Programming, ICALP 2025, Aarhus, Denmark Leibniz International Proceedings in Informatics, LIPIcs Type: main |
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