Static complexity of weighted diameter relative to APSP

Determine the relationship between the computational complexity of static weighted-graph diameter and all-pairs shortest paths, resolving whether static weighted diameter admits a substantially faster algorithm than APSP.

Background

The paper contrasts static and sensitivity versions of graph diameter. It notes that decremental diameter in weighted graphs is conditionally hard, while the corresponding complexity of the static problem relative to APSP is unresolved. Establishing whether static weighted diameter is genuinely easier than APSP would clarify the benchmark against which sensitivity algorithms are compared.

References

In weighted graphs, decremental diameter is hard under the APSP hypothesis , while its static relationship to APSP remains an open question.

— The Cost of Changing Edges for Diameter Computation and More  (2608.12628 - Hiken et al., 12 Aug 2026) in Section 1, “Some Wishful Thinking”