Reduction from Directed, Weighted APSP to Replacement Paths Problem (RPP)
Revision as of 11:55, 15 February 2023 by Admin (talk | contribs) (Created page with "FROM: Directed, Weighted APSP TO: Replacement Paths Problem (RPP) == Description == == Implications == if: to-time: $T(n) polylog M$ in graphs with integer weights in $({0}, M)$<br/>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/10.1145/318...")
FROM: Directed, Weighted APSP TO: Replacement Paths Problem (RPP)
Description
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