In this work, we prove a $\tilde{\Omega}(\lg^{3/2} n )$ unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge insertions. This is the first super-logarithmic lower bound for any natural graph problem. In proving the lower bound, we also make novel contributions to the state-of-the-art data structure lower bound techniques that we hope may lead to further progress in proving lower bounds.

翻译：本文证明了在边插入操作下，支持$n$节点有向无环图中可达性查询的动态数据结构中，查询时间与更新时间最大值存在$\tilde{\Omega}(\lg^{3/2} n)$的无条件下界。这是首个针对自然图问题的超对数下界。在证明该下界的过程中，我们还对现有数据结构下界技术做出了创新性贡献，期望这些贡献能推动下界证明领域的进一步发展。