Reduction from Matrix Product to Negative Triangle Detection

FROM: Matrix Product TO: Negative Triangle Detection

Description

Multiplying rectangular matrices

Implications

if: to-time: $T(n)$
then: from-time: $O(mp\cdot T(n^{1/3}) \log W)$ s.t. $mp \leq n^{3}$ and $\sqrt{p} \leq m \leq p^{2}$ and multiplying two matrices of dimensions $m \times n$ and $n \times p$ over $R$ and $W$ 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 4.4