Reduction from Negative Triangle to Price Query

FROM: Negative Triangle TO: Price Query

Implications

if: to-time: $O(n^{2} / f(n))$ to answer any subsequent price query after $n$-node edge-weighted graph is preprocessed in $O(^k)$ time for some constant $k > {0}$
then: from-time: $O(n^{3} / f(n^{1/({2}k)})$

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 1.5