Reduction from Matrix Product to Negative Triangle Detection: Difference between revisions
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== Description == | == Description == | ||
Multiplying rectangular matrices | |||
== Implications == | == Implications == | ||
if: to-time: $ | if: to-time: $T(n)$<br/>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 == | == 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 4.4 | ||
Revision as of 09:58, 10 April 2023
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