Reduction from Reach Centrality to Diameter: Difference between revisions
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(Created page with "FROM: Reach Centrality TO: Diameter == Description == == Implications == == 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/10.1137/1.9781611...") |
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== Description == | == Description == | ||
For directed graphs only | |||
== Implications == | == Implications == | ||
if: to-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge directed graph with integer weights in $(-M,M)$<br/>then: from-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge directed graph with integer weights in $(-M,M)$ | |||
== Year == | == Year == | ||
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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. | 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, | https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Lemma 3.2 | ||
Revision as of 11:55, 15 February 2023
FROM: Reach Centrality TO: Diameter
Description
For directed graphs only
Implications
if: to-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge directed graph with integer weights in $(-M,M)$
then: from-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge directed 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 3.2