Reduction from Matrix Product to Negative Triangle Detection

FROM: Matrix Product TO: Negative Triangle Detection

Description

Generic runtimes for two $n \times n$ matrices

Implications

if: to-time: $T(n)$ where $T(n)/n$ is decreasing
then: from-time: $O(n^{2} \cdot T(n^{1/3})\log W)$ for two $n\times n$ matrices where $W$ is the maxint of $R$

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 4.2