Reduction from Negative Triangle Detection to All-Nodes Positive Betweenness Centrality

FROM: Negative Triangle Detection TO: All-Nodes Positive Betweenness Centrality

Implications

if: to-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge graph with integer weights in $(-M,M)$
then: from-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge graph with integer weights in $(-M,M)$

Year

2015

Reference

Amir Abboud, Fabrizio Grandoni, and Virginia Vassilevska Williams. Subcubic equivalences between graph centrality problems, APSP and diameter. In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4-6, 2015, pages 1681–1697, 2015.

https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Lemma 4.4