Reduction from Negative Triangle Detection to Shortest Cycle

FROM: Negative Triangle Detection TO: Shortest Cycle

Implications

if: to-time: $T(n,M)$ where there are $n$ nodes and weights in $({1}, M)$
then: from-time: $T(n, O(M))$ where there are $n$ nodes and weights in $(-M, M)$

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 5.3