Reduction from Directed, Weighted APSP to Replacement Paths Problem (RPP)

FROM: Directed, Weighted APSP TO: Replacement Paths Problem (RPP)

Implications

if: to-time: $T(n) polylog M$ in graphs with integer weights in $({0}, M)$
then: from-time: $O(n^{2} T(O(n^{1/3})) polylog M)$ in graphs with integer 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, Corollary 5.1