Directed–undirected separation for static graph problems

Prove or refute the existence of a computational separation between directed and undirected versions of the static graph problems considered, particularly static diameter approximation.

Background

The paper establishes different conditional lower bounds for incremental diameter and related parameters in directed and undirected graphs. It emphasizes that an analogous separation in the static setting is unresolved: known lower-bound techniques have transferred directed hardness to undirected graphs, while the best directed and undirected upper bounds remain substantially different.

References

We highlight that such a separation is still a big open problem in the static setting.

— The Cost of Changing Edges for Diameter Computation and More  (2608.12628 - Hiken et al., 12 Aug 2026) in Section 1, “Our Results for the Incremental Setting”