Since 1989, the best known lower bound on static data structures was Siegel's classical cell sampling lower bound. Siegel showed an explicit problem with $n$ inputs and $m$ possible queries such that every data structure that answers queries by probing $t$ memory cells requires space $s\geq\widetilde{\Omega}\left(n\cdot(\frac{m}{n})^{1/t}\right)$. In this work, we improve this bound for non-adaptive data structures to $s\geq\widetilde{\Omega}\left(n\cdot(\frac{m}{n})^{1/(t-1)}\right)$ for all $t \geq 2$. For $t=2$, we give a lower bound of $s>m-o(m)$, improving on the bound $s>m/2$ recently proved by Viola over $\mathbb{F}_2$ and Siegel's bound $s\geq\widetilde{\Omega}(\sqrt{mn})$ over other finite fields.
翻译:自1989年以来,对静态数据结构最已知的较低约束范围是 Siegel 的经典单元格取样较低约束范围。 Siegel 在输入美元和可能查询美元方面显示出一个明显的问题,因此通过对美元存储单元格进行查询而回答询问的每个数据结构都需要空间 $\ gq\ loblytilde\ Omega left(n\ geq{ {n})\\\ t\ t ⁇ right) 。 在这项工作中,我们将非适应性数据结构对非适应性数据结构的约束改进到 $\ geq\ lobleft(n\ cd@\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\