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.

翻译：在以美元为单位的超立方体垃圾包装问题中,必须把一个以美元为单位的超立方体填入最小数量的超立方体中。 Epstein和van Stee[SIAM J.Compuut.35 (2005年)]表明,在线捆绑式空间变体的无症状性能比为$-Omega(log d)美元和$-O(d/\log d)美元,并假定这是$-Theta(\log d)美元。我们用概率论来表明,美元实际上是$-theta(d/\log d)美元。