Reduction from Matrix Product to Negative Triangle Detection

FROM: Matrix Product TO: Negative Triangle Detection

Description

$n \times n$ matrices and triangle problem over $R$ Corollary to generic runtimes

Implications

if: to-time: $O(n^{3}/\log^c n)$ for some constant $c$
then: from-time: $O((\log W) n^{3} / \log^c n)$ where $W$ is 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, Corollary 4.1