Reduction from Minimum Triangle to Second Shortest Simple Path

FROM: Minimum Triangle TO: Second Shortest Simple Path

Implications

if: to-time: $T(n,W)$ where there are $n$ nodes and integer weights in $({0}, W)$
then: from-time: $T(O(n), O(nW))$ for $n$ node graph with integer weights in $(-W, W)$

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 5.5