Packing $d$-dimensional balls into a $d + 1$-dimensional container

Alt, Helmut (avtor), Cabello, Sergio (avtor), Cheong, Otfried (avtor), Park, Ji-won (avtor), Seiferth, Nadja (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: packings, translations, unit disks, unit balls, volume
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: 13 str.
• Številčenje: Vol. 132, art. 102219
• PID: 20.500.12556/RUL-176508
• UDK: 004.92:514
• ISSN pri članku: 0925-7721
• DOI: 10.1016/j.comgeo.2025.102219
• COBISS.SI-ID: 259634179
• Datum objave v RUL: 02.12.2025

Gradivo je del revije

• Naslov: Computational geometry
• Skrajšan naslov: Comput. geom.
• Založnik: Elsevier
• ISSN: 0925-7721
• COBISS.SI-ID: 14903301

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.