Reduction from Matrix Product to Negative Triangle Detection: Difference between revisions
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== Description == | == Description == | ||
$n | Generic runtime but with $T(n)$ s.t. $T(n)/n^2$ is decreasing | ||
== Implications == | == Implications == | ||
if: to-time: $ | if: to-time: $T(n)$ where $T(n)/n^{2}$ is decreasing<br/>then: from-time: $O(n^{2} \cdot T(n^{1/3})\log n)$ for two $n\times n$ matrices with high probability | ||
== Year == | == Year == | ||
| Line 18: | Line 17: | ||
V. V. Williams, R. R. Williams, Subcubic Equivalences Between Path, Matrix, and Triangle Problems. 2018. | V. V. Williams, R. R. Williams, Subcubic Equivalences Between Path, Matrix, and Triangle Problems. 2018. | ||
https://dl.acm.org/doi/pdf/10.1145/3186893, | https://dl.acm.org/doi/pdf/10.1145/3186893, Theorem 4.5 | ||
Latest revision as of 10:45, 28 April 2023
FROM: Matrix Product TO: Negative Triangle Detection
Description
Generic runtime but with $T(n)$ s.t. $T(n)/n^2$ is decreasing
Implications
if: to-time: $T(n)$ where $T(n)/n^{2}$ is decreasing
then: from-time: $O(n^{2} \cdot T(n^{1/3})\log n)$ for two $n\times n$ matrices with high probability
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 4.5