Establish lower bounds for depth-first search in CONGEST

Establish nontrivial lower bounds on the randomized round complexity of computing a depth-first search traversal/tree in the CONGEST model.

The paper surveys problems where known upper bounds exist but lower bounds are lacking, highlighting DFS as a notable case.

They explicitly point out the absence of any lower bound for DFS, contrasting it with an existing upper bound of ~O(√(Dn)+n^{3/4}).

For depth-first search, the state-of-the-art upper bound is \widetilde{O}(\sqrt{Dn} + n^{3/4}), but no lower bound is known.

— Optimal Distributed Replacement Paths (2502.15378 - Chang et al., 21 Feb 2025) in Section: Conclusions and Open Problems (Further lower bounds)