Approximate Reach Centrality (Vertex Centrality)
Revision as of 10:28, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Approximate Reach Centrality (Vertex Centrality)}} == Description == The reach centrality of a node $w$ is the smallest distance $r$ such that any $s-t$ shortest path passing through $w$ has either $s$ or $t$ in the ball of radius $r$ around $w$. Approximate reach centrality is the approximation version of the problem. == Related Problems == Generalizations: Reach Centrality Related: Eccentricity, All-Nodes Median Parity, Betweenness C...")
Description
The reach centrality of a node $w$ is the smallest distance $r$ such that any $s-t$ shortest path passing through $w$ has either $s$ or $t$ in the ball of radius $r$ around $w$.
Approximate reach centrality is the approximation version of the problem.
Related Problems
Generalizations: Reach Centrality
Related: Eccentricity, All-Nodes Median Parity, Betweenness Centrality, Approximate Betweenness Centrality, Positive Betweenness Centrality, Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality, Directed All-Nodes Reach Centrality, Undirected All-Nodes Reach Centrality
Parameters
n: number of vertices m: number of edges
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| CNF-SAT | if: to-time: $O(m^{2-\epsilon})$ for some $\epsilon > {0}$ then: from-time: $O*({2}^{({1}-\delta)n})$ for some $\delta > {0}$ |
2015 | https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Corollary 4.2 | link |
| CNF-SAT | if: to-time: $O(m^{2-\epsilon})$ then: from-time: $O*({2}^{({1}-\epsilon/{2})n})$ |
2015 | https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Theorem 4.4 | link |