| Naslov: | Packing $d$-dimensional balls into a $d + 1$-dimensional container |
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| Avtorji: | ID Alt, Helmut (Avtor)
ID Cabello, Sergio (Avtor)
ID Cheong, Otfried (Avtor)
ID Park, Ji-won (Avtor)
ID Seiferth, Nadja (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (1,01 MB)
MD5: 0B37C1C4CBA562D3CE602CE909955EC7
 URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0925772125000574
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | 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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| Ključne besede: | packings, translations, unit disks, unit balls, volume |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.05.2026 |
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| Leto izida: | 2026 |
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| Št. strani: | 13 str. |
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| Številčenje: | Vol. 132, article no. 102219 |
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| PID: | 20.500.12556/DiRROS-24501  |
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| UDK: | 004.92:514 |
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| ISSN pri članku: | 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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| Opomba: |
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| Datum objave v DiRROS: | 02.12.2025 |
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| Število ogledov: | 93 |
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| Število prenosov: | 46 |
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| Metapodatki: |    |
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