Reduction from Negative Triangle Listing to Negative Triangle Detection

FROM: Negative Triangle Listing TO: Negative Triangle Detection

Implications

if: to-time: $O(n^{3-\epsilon}\log^c M)$ for some $\epsilon > {0}$ and where $M$ is the maxint of $R$
then: from-time: $O(n^{3-\epsilon'}\log^c M)$ for some $\epsilon' > {0}$ for listing $\Delta = O(n^{3-\delta})$ negative triangles with fixed $\delta > {0}$

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 4.3