Reduction from Matrix Product to Negative Triangle Detection

From Algorithm Wiki
Revision as of 11:55, 15 February 2023 by Admin (talk | contribs) (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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

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
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.org/doi/pdf/10.1145/3186893, Theorem 4.2