更强的3SUM-索引下界
Stronger 3SUM-Indexing Lower Bounds
摘要：
$3$ SUM-索引问题是作为$3$ SUM问题的数据结构版本引入的，其目标是通过归约来证明静态数据结构的强条件下界。理想情况下，$3$ SUM-分度的约束硬度应该由无条件下限代替。不幸的是，我们还远没有证明这一点，目前最强的下限是Golovnev等人在STOC'20中提出的对数查询时间下限。此外，他们的下限仅适用于非自适应数据结构，并且他们明确要求自适应数据结构的下限。我们的主要贡献正是这样一个下界对自适应数据结构。作为第二个结果，我们还加强了Golovnev等人的非自适应下界。并通过一种全新的方法证明了$2$ -位探测非自适应$3$ SUM-索引数据结构的强下界，我们发现它本身很有趣。
英文摘要：
The $3$SUM-Indexing problem was introduced as a data structure version of the $3$SUM problem, with the goal of proving strong conditional lower bounds for static data structures via reductions. Ideally, the conjectured hardness of $3$SUM-Indexing should be replaced by an unconditional lower bound. Unfortunately, we are far from proving this, with the strongest current lower bound being a logarithmic query time lower bound by Golovnev et al. from STOC'20. Moreover, their lower bound holds only for non-adaptive data structures and they explicitly asked for a lower bound for adaptive data structures. Our main contribution is precisely such a lower bound against adaptive data structures. As a secondary result, we also strengthen the non-adaptive lower bound of Golovnev et al. and prove strong lower bounds for $2$-bit-probe non-adaptive $3$SUM-Indexing data structures via a completely new approach that we find interesting in its own right.
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