A tight lower bound for the online bounded space hypercube bin packing problem
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 $\Om...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
Discrete Mathematics & Theoretical Computer Science
2021-09-01
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Series: | Discrete Mathematics & Theoretical Computer Science |
Subjects: | |
Online Access: | https://dmtcs.episciences.org/8325/pdf |
Summary: | 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. |
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ISSN: | 1365-8050 |