Reduction from Distance Product to Second Shortest Simple Path
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FROM: Distance Product TO: Second Shortest Simple Path
Description
Implications
if: to-time: $T(n,W)$ where there are $n$ nodes and integer weights in $({0}, W)$
then: from-time: $O(n^{2} T(O(n^{1/3}), O(nW)) \log W)$ for two $n\times n$ matrices with 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