A tight lower bound for the online bounded space hypercube bin packing problem

Abstract

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.

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