On-line Packing Cubes into $n$ Unit Cubes

Volume 64 / 2016

Łukasz Zielonka Bulletin Polish Acad. Sci. Math. 64 (2016), 185-198 MSC: Primary 52C17; Secondary 05B40. DOI: 10.4064/ba8063-10-2016 Published online: 24 November 2016


If $n\geq 3$ and $d\in \{3,4\}$ or if $n\geq 1$ and $d\geq 5$, then any sequence of $d$-dimensional cubes of edge lengths not greater than $1$ whose total volume does not exceed $(n+1)\cdot 2^{-d}$ can be on-line packed into $n$ unit $d$-dimensional cubes.


  • Łukasz ZielonkaInstitute of Mathematics and Physics
    UTP University of Science and Technology
    Kaliskiego 7
    85-789 Bydgoszcz, Poland

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