Reduction from Matrix Product to Negative Triangle Detection: Difference between revisions
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== Description == | == Description == | ||
Generic runtime but with $T(n)$ s.t. $T(n)/n^2$ is decreasing | |||
== Implications == | == Implications == | ||
if: to-time: $T(n)$<br/>then: from-time: $O( | 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 == | ||
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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, Theorem 4. | https://dl.acm.org/doi/pdf/10.1145/3186893, Theorem 4.5 | ||
Revision as of 09:58, 10 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