Super-Logarithmic Lower Bounds for Dynamic Graph Problems - Larsen, Kasper Green; Yu, Huacheng (Proceedings / annual Symposium on Foundations of Computer Science, 2023)
In this work, we prove a \tilde{Ω}(\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.