## 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 problem

Authors: Yoshiharu Kohayakawa ; Flávio Keidi Miyazawa ; Yoshiko Wakabayashi

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.

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