Distance Sensitivity Oracle matching Williams’s APSP runtime

Construct a distance sensitivity oracle with preprocessing time matching Williams’s all-pairs shortest-path runtime, or otherwise achieve subcubic preprocessing time for a distance sensitivity oracle.

Background

The paper uses distance sensitivity oracles as a central tool for decremental diameter and eccentricity algorithms. It observes that, unlike the incremental setting, obtaining a decremental oracle with preprocessing comparable to the best known APSP algorithms—or even any subcubic preprocessing bound—remains unresolved.

References

(For instance, developing a DSO with a preprocessing time that directly matches Williams' APSP time , or simply achieving an $o(n3)$ runtime, remains an interesting open problem, whereas this is easily achievable in the incremental 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”