Geodesic
A tight lower bound for the online bounded space hypercube bin packing problem
Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 3.

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In the $d$-dimensional hypercube bin packing problem, a given list of $d$-dimensional hypercubes must be packed into the smallest number of hypercube bins. Epstein and van Stee [SIAM J. Comput. 35 (2005)] showed that the asymptotic performance ratio $\rho$ of the online bounded space variant is $\Omega(\log d)$ and $O(d/\log d)$, and conjectured that it is $\Theta(\log d)$. We show that $\rho$ is in fact $\Theta(d/\log d)$, using probabilistic arguments.
DOI : 10.46298/dmtcs.8325
Classification : 05C70 
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     title = {A tight lower bound for the online bounded space hypercube bin packing problem},
     journal = {Discrete mathematics & theoretical computer science},
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Kohayakawa, Yoshiharu; Miyazawa, Flávio Keidi; Wakabayashi, Yoshiko. A tight lower bound for the online bounded space hypercube bin packing problem. Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 3. doi : 10.46298/dmtcs.8325. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.8325/

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