Extending the SSBP lower bound from n updates to n^2 updates

Extend the conditional lower bound for incremental/decremental Single Source Bottleneck Paths (SSBP) on directed graphs—currently shown to require n^{2.5−o(1)} total update time over n updates under the Minimum-Witness Product hypothesis—to hold for n^2 updates.

Background

The paper proves that, assuming the Minimum-Witness Product hypothesis, any partially dynamic SSBP algorithm requires n^{2.5−o(1)} total update time over only n updates by reducing from min-witness product. This establishes a strong barrier for achieving faster partially dynamic SSBP in this regime.

However, the reduction and resulting lower bound presently apply to n updates; extending this conditional lower bound to n^2 updates would match more typical dynamic settings and further solidify the hardness landscape for SSBP.