Yoshiharu Kohayakawa ; Flávio Keidi Miyazawa ; Yoshiko Wakabayashi - A tight lower bound for the online bounded space hypercube bin packing problem

dmtcs:8325 - Discrete Mathematics & Theoretical Computer Science, September 14, 2021, vol. 23, no. 3 - https://doi.org/10.46298/dmtcs.8325
A tight lower bound for the online bounded space hypercube bin packing problemArticle

Authors: Yoshiharu Kohayakawa ORCID; Flávio Keidi Miyazawa ; Yoshiko Wakabayashi ORCID

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.

Comment: This manuscript is derived from arXiv:1712.06763, where further material is presented and the proofs are formulated a little differently

https://doi.org/10.46298/dmtcs.8325
Source: arXiv.org:2107.14161
Volume: vol. 23, no. 3
Section: Discrete Algorithms
Published on: September 14, 2021
Accepted on: August 20, 2021
Submitted on: July 30, 2021
Keywords: Mathematics - Combinatorics, Computer Science - Discrete Mathematics, 68Q17, 68W27, 68W25, 52C17, 05D40
Licence: Attribution-Non Commercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

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Mathematics Subject Classification 20201
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