| Title: | Packing $d$-dimensional balls into a $d + 1$-dimensional container |
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| Authors: | ID Alt, Helmut (Author)
ID Cabello, Sergio (Author)
ID Cheong, Otfried (Author)
ID Park, Ji-won (Author)
ID Seiferth, Nadja (Author) |
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| Files: |  PDF - Presentation file, download (1,01 MB)
MD5: 0B37C1C4CBA562D3CE602CE909955EC7
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0925772125000574
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | In this article, we consider the problems of finding in $d + 1$ dimensions a minimum-volume axis-parallel box, a minimum-volume arbitrarily-oriented box and a minimum-volume convex body into which a given set of $d$-dimensional unit-radius balls can be packed under translations. The computational problem is neither known to be NP-hard nor to be in NP. We give a constant-factor approximation algorithm for each of these containers based on a reduction to finding a shortest Hamiltonian path in a weighted graph, which in turn models the problem of stabbing the centers of the input balls while keeping them disjoint. We also show that for $n$ such balls, a container of volume $O(n^{d−1 \over d})$ is always sufficient and sometimes necessary. As a byproduct, this implies that for $d \ge 2$ there is no finite size $(d + 1)$-dimensional convex body into which all $d$-dimensional unit-radius balls can be packed simultaneously. |
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| Keywords: | packings, translations, unit disks, unit balls, volume |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.05.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 13 str. |
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| Numbering: | Vol. 132, article no. 102219 |
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| PID: | 20.500.12556/DiRROS-24501  |
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| UDC: | 004.92:514 |
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| ISSN on article: | 0925-7721 |
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| DOI: | 10.1016/j.comgeo.2025.102219 |
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| COBISS.SI-ID: | 259634179 |
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| Note: |
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| Publication date in DiRROS: | 02.12.2025 |
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| Views: | 94 |
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| Downloads: | 50 |
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| Metadata: |    |
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