Reduction from Directed, Weighted APSP to Second Shortest Simple Path

FROM: Directed, Weighted APSP TO: Second Shortest Simple Path

Implications

if: to-time: $T(n,W)$ where there are $n$ nodes and integer weights in $({0}, W)$
then: from-time: $O(n^{2} T(O(n^{1/3}), O(n^{2}W)) \log Wn)$ for graphs with weights in $(-W, W)$

Year

2018

Reference

V. V. Williams, R. R. Williams, Subcubic Equivalences Between Path, Matrix, and Triangle Problems. 2018.

https://dl.acm.org/doi/pdf/10.1145/3186893, Theorem 5.5