Super-Logarithmic Lower Bounds for Dynamic Graph Problems

04/18/2023

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by   Kasper Green Larsen, et al.

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In this work, we prove a Ω̃(^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.