Reduction from Matrix Product to Negative Triangle Detection
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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