Reduction from Matrix Product to Negative Triangle Detection: Difference between revisions
Jump to navigation
Jump to search
(Created page with "FROM: Matrix Product TO: Negative Triangle Detection == Description == Generic runtimes for two $n \times n$ matrices == Implications == if: to-time: $T(n)$ where $T(n)/n$ is decreasing<br/>then: from-time: $O(n^{2} \cdot T(n^{1/3})\log W)$ for two $n\times n$ matrices where $W$ 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.o...") |
No edit summary |
||
Line 3: | Line 3: | ||
== Description == | == Description == | ||
$n \times n$ matrices and triangle problem over $R$ | |||
Corollary to generic runtimes | |||
== Implications == | == Implications == | ||
if: to-time: $ | if: to-time: $O(n^{3}/\log^c n)$ for some constant $c$<br/>then: from-time: $O((\log W) n^{3} / \log^c n)$ where $W$ is maxint of $R$ | ||
== Year == | == Year == | ||
Line 17: | Line 18: | ||
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, Corollary 4.1 |
Revision as of 11:55, 15 February 2023
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