Reduction from Undirected, Weighted APSP to Directed, Weighted APSP

FROM: Undirected, Weighted APSP TO: Directed, Weighted APSP

Implications

if: to-time: $T(n, M)$ where graph has weights in $({0}, M)$
then: from-time: $T(n, \Theta(M))$ where digraph has weights in $(-M, M)$

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 5.1