Reduction from CNF-SAT to Approximate Reach Centrality: Difference between revisions

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== Description ==  
== Description ==  


$\alpha$-approximation for any finite $\alpha$ (possibly depending on $m$)
$(2-\epsilon)$-approximation in undirected, unweighted graphs for some constant $\epsilon > 0$


== Implications ==  
== Implications ==  


if: to-time: $O(m^{2-\epsilon})$ for some $\epsilon > {0}$<br/>then: from-time: $O*({2}^{({1}-\delta)n})$ for some $\delta > {0}$
if: to-time: $O(m^{2-\epsilon})$<br/>then: from-time: $O*({2}^{({1}-\epsilon/{2})n})$


== 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, Corollary 4.2
https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Theorem 4.4

Revision as of 12:19, 15 February 2023

FROM: CNF-SAT TO: Approximate Reach Centrality

Description

$(2-\epsilon)$-approximation in undirected, unweighted graphs for some constant $\epsilon > 0$

Implications

if: to-time: $O(m^{2-\epsilon})$
then: from-time: $O*({2}^{({1}-\epsilon/{2})n})$

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, Theorem 4.4